The subject dll is a basic "Windows has an error" and does not tell what to do next. Your post mentions use of System Restore, but doesn't tell why this was done.
No clues means that any guess may be wrong. However I will offer "What I would do."
1. Go get IEFIX from google.com and use it. It repairs many errors without us finding the specific item.
2. "Now I cannot get on the internet due to dll errors one of which is kernel32.dll. What can I do?"
Tell exactly what you are doing at the time of the error. Booting up? Running intenet explorer?
Have Compaq Pressario 5000 system but don't have original monitor. On 11/27/04 I performed system restore back to April 2004 which was before I replaced the monitor. Now I cannot get on the internet due to dll errors one of which is kernel32.dll. What can I do?