Windows XP, as well as Windows 2000 is an operating system that was released when the Classic- Tomb Raider Games were already on the market. In some cases they are not compatible with it, meaning that the game might crash after being started or not start at all.
There are a few things you can try:
1. I recommend, that you install the latest Service Packs, get new drivers for your graphic card, install the latest DirectX Version.
2. Rightclick on the tomb.exe and choose compatibility mode Windows 98 (or Windows 95)
The tomb.exe can be found in the Program folder on your hard drive (not on the CD).
Example: c:\program files\Core Design\Tomb Raider II\
here you would have to find the tomb2.exe
(In other cases you are looking for the tomb3.exe, tomb4.exe ...)
If you don't have this exe, you have probably turned off the file-extensions. Turn them on!!!