Laptop will not boot

Hello, I have an IBM ThinkPad R51 and it just recently it stopped working. It was working fine and then the screen froze. I did a hard reboot but it does not show anything on the screen (the power and battery light comes on) and it did not go through its POST with no hard drive activity. I turn it on and off and sometimes it will display the IBM screen and I am able to put in the boot up password and I am able to log in to Windows (XP) but after a second or two, it freezes again. I tested the hard drive in my other ThinkPad R51 and it works perfectly for hours. I also replaced the memory in the defective one and it came up for a few minutes and then I get like a small static (for a second or two) on the screen and it freezes again and sometimes the screen will go black and then back to the frozen screen. When I can get the IBM boot screen, (maybe every 15 or 20 tries or if I leave it for a few hours) it will not allow me to get into the BIOS screen because I get that static and it freezes again. The hard drive is working and the memory is OK (I even swapped memory and memory slots). I cannot figure out what is the problem. Is it a video connection (I removed the keyboard and reconnected the video connection)? Would a video problem cause the freezing? Thanks for any help you can provide.