Well, the problem with the video card is more likely the drivers themselves rather than the laptop or even the OS. For example, Microsoft's drivers tend to suck (in my opinion)... I had to go back and use ATI's driver package, and I couldn't even use the latest one because of slight issue with my video card and the driver, but I did find a workable driver from them (wasn't the latest release, but a more recent driver).
Point being that to say that you want to run Linux because of video card/driver issues won't neccesarily solve the problem. You could very well run into the same problem on a Linux box/laptop.
Now, to answer your question...
I have a Dell Inspirion 11z (sort of the size of a netbook) but has a 1.3 GHz dual core proc, runs for about 4-5 hours on a battery charge, you can get them with large drives, or you can upgrade them yourself (Dell is the only company I know of that still gives you a Windows restore-CD, whereas most others just have a partition on the HD, which is sort of pointless if hard your disc dies--some PCs also have a utility to create a recovery DVD set too but not too many).
Anyway, I'm very pleased with my Dell. It cost me about $450 shipped to my door (and included any sales tax ,etc). Yes, it isn't the fastest laptop out there, but I was more for portability, battery life, and durability--Some Dells are very sturdy, and I feel the 11z is a good choice for all of these criteria. Now, it may run you a little over $500 to get one with a 200+ GB hard drive and 4GB of RAM, but you can also do the upgrades yourself as well. It runs Windows 7 perfectly fine. It can get glitchy, though, if you're multitasking a lot (like watching a video and ripping a CD for example), so if you like to run a lot of programs at once, you may want to go for the 4GB of RAM. It has on-board video, but it can play some games, but probably not the latest games).
Another computer I had, costed a little more, was a Lenovo ThinkPad SL series. Also a good computer, but a bit more heavy. Now, the one that I had was about 3 years ago, so I don't know how well they are today, but Lenovo Thinkpads have usually been known for quality and durability as for many companies use them for their employees. They may not be the cheapest or fastest, but their tech support is good and they are geared towards those who are looking for durability and reliability over performance and features. Their systems are a bit bland, especially the cheaper ones, but still a brand worth looking into.
Basically, don't get a netbook or even the $300 laptops you see at WalMart or BestBuy. These, in my opinion, are junk and will only last 3 years before you have to do something to them. The only exception would be the Inspiron like i described. I've not had an issue with mine (knock on wood) but over the past 3 Dells I have had, I've never had to call warranty on any of them. My Lenovo Thinkpad I had to call support once one becaus ethe WLAN burnt out (but that was probably due to me dropping it once because it occured no more than 3 days after the drop when I went to use the WLAN again).
I would stay away from Acer, Gateway, EMachines, etc. The low-end of the market. Yes, many of their units are feature-packed, but my concern is more with build quality than features with these brands. Basically ,it comes down to what you like and how much you want to spend. I wouldn't bother on an extended warranty much beyond 2 years, because they cost so much, you could probably buy a new one after that period for just a little more--unless they give you a deal on the extended warranty, like 3 years parts/labor for 25% of the value of the computer... then maybe, but I generally don't get extended warranties on PCs/laptops under $500. If it was a car or something of more moneytary value, then by all means yes, but laptops have become so inexpensive these days, it almost makes no sense to pay the extra money.
By the way, the Dell is easy to upgrade the HD and RAM because it's all under the keyboard and requires you to remove only 3 screws. Took me only 5 minutes to remove the RAM and HD out of my Inspiron 11z. Also, getting one with an LED display also helps battery a bit. The 11z has an LED backlight, it's only an 11.6" screen, but for portability it's perfect and the keyboard isn't like those on a netbook where even people with small hands can't type. The 11z has a decent sized keyboard (not quite as big as a full sized 15" laptop, but then again, the unit itself is smaller so the keyboard has to be a bit smaller as well.
Good luck in your search and be sure to ask questions here if you need more help. There is plenty of people here who can help. As for the dual boot, you can dual boot almost anything. Only problem with my 11z is it doesn't have a built-in optical drive, but I'm OK with that because I got a large HDD so I can offload my videos onto that, so I only use my USB DVD burner every once in a while for the laptop.