|It sounds like your CD drive might be marginally bad. |
Another 'less likely' possibility is a memory problem. You could try running memtest86:
There is a version to create a bootable floppy diskette and/or an ISO for creating a CD.
Run it overnight and any failures are unacceptable.
By the way, skipping files during an install is not a good idea. An install should run flawlessly.
You could 'try' a cleaning disk on the CD drive.