I am graduating with a B.S. in Computer Science from University of
Delaware in May, 2003.  I am trying to find a good full-time job where
I can work right from my apartment in Newark, Delaware after I
graduate.  I am a working musician right now, so having a traditional
day-job is not an option (as a result of my rigorous gigging/touring
schedule).  I need to work on flexible hours from my apartment where I
will have a DSL connection.  My best areas of computing skills are in
web-design and databases.  A list of companies/people/places where I
could send my resume would be quite helpful.  Thanks!

In addition to whatever the researchers pass to you,
you should remember that much of your search is
going to be 'job' specific, meaning that 1000s of
companies might allow you to do this, but it is a 
question of when a job appears.  Also, this could
become a negotiation for you, meaning that you find
a job and negotiate it accomodating your schedule.
Hope you get to play at the Stone Balloon if it is still there.

Have you time to look up job sites yourself? Maybe you could look up these sites:

Telecommuting Jobs
http://www.tjobs.com 

Telework Connection - Find Telecommuting jobs
http://www.telework-connection.com/job-sites.htm

Try searching "telecommuting jobs" or "freelance telecommuting" on Google.