Did you shut down all non-essential programs (especially anti-virus) before starting the install? It may help to run it as administrator (right click on the executable).
In Windows Explorer, can you manually copy the file(s) mentioned in the error(s) to the appropriate place on the hard drive?
If you still have your old computer, try re-installing the game there, to confirm there has not been a problem with the disk itself (like a scratch, or something). If it still installs fine with the old system, there may be a conflict with the new optical drive, or some program running in the background.
If D2:ED is still on the old computer, you could try copying the whole folder to the new computer (over a network, or on a USB drive, etc).
