You rather blew by some of the questions that have been asked but I'll throw out the following.
The Dell Dimension 1100 is an entry level PC and I believe the soundcard is integrated into the motherboard. The line level analog input of the card could be your limitation. (This assumes that the Onkyo cassette deck is giving good results when you play a cassette back directly through your stereo.)
However, it is still worth checking that you have the correct adapter cable going to the correct input. You should also check your driver and input settings for the soundcard on the PC. I don't use Nero for recording, but double-check your software settings there, too.
Do you have any other analog input sources you can try with the PC (a turntable or tuner, for example)? If you get poor results recording other analog sources to CD then you likely need to look at the computer end of things.
Good luck.