Microsoft Excel 2000

One thing about Excel is that it's a real memory hog. If you have a lot of other programs open, or a lot of spreadsheets, you can sometimes see memory errors. Does it happen when all other programs are closed? When you're copy/pasting only a little text (say, only a few cels versus an entire spreadsheet)? When you only have one file open? If it does, then I'd be concerned about possibly something else drawing on your memory. But if it doesn't happen under those conditions, then you may be legitimately maxing out your PC.

Microsoft Excel 2000
No other applications are opened. I have only Excel 2000 open. The error occurs when I try and one cell or multiple cells.

I had a customer with this problem, but they were using Microsoft Terminal Services, which has hooks into the clipboard.

You might try finding a clipboard replacement.

http://www.tucows.com/search?search_terms=clipboard&search_scope=win&search_adv=0&search_size=&search_size_multi=b