The answer is no, you can't do that. Sorry :-(
Windows sees users as SID strings, not user names, and they are generated randomly. If you delete a user account and then re-create it, it will generate a different SID for that user, and that user will be a separate, distinct person from the first -- even if you use the same account name and everything.
You CAN, however, figure out which SID belonged to which user by looking in the registry of the old server (if you still have it around). You just mount the SYSTEM hive and navigate to HKLM\SOFTWARE\Microsoft\Windows NT\CurrentVersion\ProfileList. Each SID known to the old server will show the location of that user's profile folder (and hence, their account name).
That will help you rebuild the permissions on the drive, knowing who had access to what. But you cannot, under any circumstance, associate a user account to a specific SID. That would be SID spoofing and it's a security violation that Windows specifically guards against.