some more useful information would be:
What kind of files are you copying? With just 64 mb's of ram these days a word file with heavy graffics could max out the ram. In this case, I would check to make sure the size of your paging file is large enough.
Have you checked the file and any attachments for viruses or (more likely) corruption? I have seen a situation where someone's computer would lock up every time they tried to open up a specific file. Once again this turned out to be a word doc with graffical attachments. One of the corrupt graffic files was causing this. (There is no remedy to this but replace the corrupt file if you have a backup).
finally, is your hardrive making any funny noises? I am not talking about the regular crunching sound. I saw a situation where whenever a guy opened up a large file his comp would slow down to a crawl and the hardrive would make a wierd sound. The file was on the network so I was able to open it with another comp and see it was not corrupt. It turned out that switching out the hardrive in this case solved the problem.
Hope this helps