He is rather likely to have significant support due to a large number of reasons:
-First, his adminsitration was significantly less corrupt than the ones in neighbouring countries. A large part of the oil profits was invested in infrastructure, and Lybia had the 2nd highest standart of living in Africa after South Africa.
-Second: Ghadaffis own clan/tribe is small. There are a lot of positions left for non Ghadaffi Clan members, and the other comparably small tribes/ the urbanized population likes that a lot.
-Third: Repression in Lybia was going down prior to the protests.
-Fourth: Lybia has both an East West and a North South divide. Please bear in mind that East Lybia (the current rebels) were sending the 2nd largest contigent of foreign insurgents into Iraq according to wikileaks. As a Nasserist, Ghadaffi himself is absolutly no friend of Al-Quaida, as a matter of fact, Al-Quadia stated goal is to kill people like Ghadaffi.
-Fifth: If you are black, the rebels mean bad news. Ghadaffi was supporting a lot of other African countries, and Lybian universities etc. are quite good for African standarts. They also have a sizeable population of Host workers from Sub Saharan Africa (who either traveled directly to Lybia or didnt manage/didnt want to risk the risky sea transport to Malta). These imigrants were taking some "ethnic Lybian" Jobs, and the less well educated East gets hit more by it than the richer west.
-Sixt, East and West Lybia dont have a history of getting along anyway.
-Seventh: A way to (mid range) power for persons not of Ghadaffis Clan existed, and the traditional tribal leaders tend to be listened to by the regime.
-Eigth: The best rebel troops are propably those with combat experience from Iraq. Do you want to throw in your lot with them if you are a comparably secular Lybian person? Would you like to "Surrender" to them?
On the subject of corruption, I think it should be obvious to anyone who has followed the situation in Libya that Qaddafi has stolen massive amounts of wealth from his country over the years (look at the extent of assets seized, his lifestyle, the lifestyle of his family, allegations that Western oil companies had to "pay to play" in Libya, etc.) What you really mean is that low and mid level government bureaucrats stole less from citizens than they do in other African nations. That's less of an impressive accomplishment. Of course government was still incompetent, inefficient corrupt and unresponsive in Libya (isn't it everywhere though?). It was all one big patronage network.
Wasta was the only way to get anything done or get a job. Ask any Libyan about it (have you talked to any Libyans about their country before reaching a verdict on it? I have). For an example of the institutional corruption that touched every area of Libya society, read this:
As for Qaddafi's attempts at "reform", yes, it is true, some political prisoners were being released before the rebellion. I'm not sure what else they were up to, but I do know that the reforms were being lead by Qaddafi's son Saif, and they didn't effect the supreme power of the Qaddafi family. In any case, the goodwill the earned somehow didn't mean so much when Qaddafi started ordering jet fighters to drop bombs on protesting crowds.
Western Libya certainly supports the rebellion. Every major population center in the West saw protest on and before Feb 17 (except Sirte). I've already talked about Tripoli, but here's another link:
. Guerrilla activities continue in Zuara. Zilten is half under the control of the rebels. The entire Western mountain region, the Jebel Nafusa, is in open rebellion. Zawiya was in open rebellion before it was retaken by the Khamis Brigade and several hundred to several thousand residents ended up in mass graves, and still occasional attacks happen on regime forces in the area. I don't need to tell you about Misrata, the second largest city in Western Libya. Bani Walid is from what I understand largely under rebel control. The Transitional National Council in Benghazi has representatives from every major city in Western Libya. The claim that Western Libya isn't in rebellion is just totally false. The only reason the East is totally free of Qaddafi forces and the West isn't is that it was easier for Qaddafi to clamp down in the West (closer to Tripoli, more men on hand, protests started in the East). As far as I can tell, Western Libya and Eastern Libya have different tribal identities and histories, but I don't think that's effecting the course of the conflict. It's a proven fact that plenty of fighters (I don't know an exact number but I'd guess a few hundred to 1000) from Benghazi in the East are now fighting in the West in Misrata, integrated in units with Western Libyans.
You are correct that there have been an unknown number of instances in which black Libyans and African migrants have been assaulted, arrested and even killed by rebel forces and rebel sympathizing crowds. I don't know how many, but I've seen pictures. On the other hand, I've also seen pictures of black Libyans carrying guns on the front lines with the rebels. And thousands of African migrants relied on the citizens of Misrata to feed, house and protect them, while they waited to be evacuated from the port, dodging Qaddafi shells the whole time. In the meantime, Qaddafi has been letting his security forces rob African migrants and then shove them at gunpoint onto unseaworthy boats and launch them to sea. But don't take my word for that, take the UN refugee agency:
As for the old trope that the rebels are "Al Qaeda in disguise", well that just doesn't add up. The Libyan Islamic Fighting Group, which most of these claims revolve around, never numbered more than several hundred people. This group was based almost entirely in Eastern Libya, mainly in the town of Derna. One town. They sent probably about 200-250 men to Iraq (that's my guesstimate, based on proven facts from the AQI "Sinjar records", which say that 120 Libyans went to Iraq during the peak period of foreign infiltration and activity in '06/07). It's a proven fact from those records that most did not return. According to this article, the rebel militia in the town of Derna, home of the LIFG, has exactly 2 men that had contact with Al Qaeda in Iraq:
No one in the TNC has links to radical Islam, nor does Abdul Fatah Younes, the rebel commander. So what can we conclude from all this? By my best estimate, there are a few dozen to a few hundred men who have some sort of affiliation with the LIFG fighting for the rebels, and they are totally located in the Eastern part of the country. Of these a handful (like 10-20 or so) have fought in Iraq. They are part of a force tens of thousands of men, and have hardly any leadership positions. Thus your claim that the "The best rebel troops are propably those with combat experience from Iraq" is obviously not true. Your claim that supporting the rebels equates to "throwing in your lot" with Al Qaeda does not ring true.
I'd be very interested to read something that supports your claim that Qaddafi has popular support rather than ruthlessness, money and loyal thugs. I'd also be very interested to read anything that supports your claim that most anti-Qaddafi Libyans want sharia law. But right now it seems like you're making "educated guess" which are actually not sufficiently educated.
