When you jump start your 91 accord you let it sit for 10 minutes then shut it off to see if it would start again. it didn't Does this mean there is a problem with the alternator or battery or both?

Sounds to me like a bad battery- check with a battery tester. The alternator can be tested at a place like Autozone, to tell if it is charging properly. They generally do this test for free, but call first. Hope this helped.