I replaced the screen on a thinkpad a few years ago. Grabbed the part off ebay. The removal and replacement took about 2 hours. I think I could have done it in 15 minutes but I was afraid of missing something so I took it real slow. Try to find a diagram of the screen connections before you start or even replacement procedure if it is out there.
The only tight spot I had was with the brightness connections -- on the T600 I had there was a mechanical slider that took a few tries until I got it seated properly. Go slow--you can do it.
Back up the hard drive first in case you fail and have to send it out for professional repair...