At any random time the computer freezes and generally the screen kind of fades to completely white or has lines, but always fades away and freezes. This usually happens a few minutes after starting the computer if the AC adapter is plugged in, and can usually last a whole battery life if it runs on battery. It does this at random times when not touching the computer, but it will always do it if the computer is jolted or bumped. This is a very annoying problem, what can I do to test what this might be? Could the inverter be going bad?

Bump, I'm still having this issue, any help would be great.

I've had to trouble shoot some LCD issues, so I'll give you my 2 cents worth here.

If a screen goes white, then the backlight and inverter are good, hence the white light. If you lose data for display, then you will see only the backlight's white light. I believe your screen is not recieving any data to display, but is fully lit up.

Plug in an external monitor. If it works fine, then good, it's not a board or card problem.
If the external monitor works the same flunky way, then it is a motherboard issue, or a video card issue (if it mounts onto the moboard)

If the external monitor works fine, then I would reseat the cable connection on the board and to the back of the LCD. A little surgery here is required, but be patient with it and keep track of all your screws. IBM's have very good connections, so they usually don't go bad. If reseating the connectors doesn't work, then gently flex the screen, and I do mean gently. If it is still flunky, then replace the cable, they are usually very stiff for durability, but they get brittle as time goes on. I am typing on a T21 TP that I replaced the backlight AND cable in. Good luck, and repost with the results.