If it takes a half hour to be recognized by Windows, there's some kind of software problem. Have you cleared the cache recently? De-fragmented the internal hard drive? Maybe even re-booted the computer? Something else is monopolizing all the computer's time.

You might try Control-Alt-Delete and selecting the Task Manager to see where all the processor time is going while it's trying to find your external drive.

Using a slower USB port than optimum might slow down data transfer but should never take 20+ hours to do a backup. Might double the backup time to maybe an hour but not much longer.