Recovering files off HD w/ Vista?

Ok, so here's my issue- I have an HP laptop that refuses to function, it hasn't turned on in 6 months. I have replaced the power cord, the battery, etc. I had been told by tech support at my school that the motherboard on HP laptops are completely unreliable and it likely fried and that I'm better off just buying a new laptop, which I did back in January. I bought a Gateway laptop w/ Windows 7 installed on it. However, I need the information off of my hard drive from my old HP laptop. I have already removed the hard drive itself, so now what? Can I just pop it into my new Gateway and expect to recover my files? The hard drive on the Gateway is virtually impossible to remove tho, it has the smallest screws to it and I fear I will mess it up trying to put it back in or I will lose the screws. Is it even possible to put a hard drive that had Windows Vista on it into a laptop w/ 7 running on it? I also don't want to take it to tech support or Best Buy to recover my information mainly because I have stuff on there that I don't want others to be able to access. I would prefer getting these files back on my own, if that's possible. Any suggestions?