Yes, you can rename the files instead of deleting them, in fact that is probably safer in case anything goes wrong, although you should be able to get them back from the recycle bin even if they were deleted of course.
Assuming your original inbox is still working you should be able to drag and drop messages from it into another mailbox. Perhaps create a new temporary one to avoid any confusion and put them all in that.
I'm assuming that you haven't got a huge number of messages sitting in your existing inbox. If you have, that could be the cause of the problem, as Eudora will start misbehaving if the system mailboxes (in, out, junk, and trash) become too large.