Well, given the little facts that were provided I'd guess that this is a video card driver issue.
The original game was something like DirectX5 or 6, TPR was similar.
The point is, that the old version prior to DX10 are NOT COMPLETELY included in Win Vista and above. You see that on the fact that you need to install DX9 on a machine to run for example CnC3.
The point why it works on one machine and does not on the other is then, that one driver is written in a good way, meaning that it directs the old functions to the new API while the other is not. I suspect the unsupported resolution of your new computer as the point where the problems occur.
So I suggest: try install DX9 and see if it works.
If it does not, try to install the most recent video driver.
If it still does not run, try to set your desktop resolution to 1024x768 and then start the game.
If it still does not run you can at least say that you tried your best
Btw: it would really help if you gave a little bit more information about your system, what machine, what cpu+gpu manufacturers etc.