Will not stay running after charging the battery

Your charging system more than likely is not working properly. You need to have it tested by a certified technician, or you can have a basic test run by your local parts store, they usually do them for free. Here is a guide that will explain this procedure: https://www.2carpros.com/articles/how-to-check-a-car-alternator

Thank you, I thought so. How much is it for getting the alternator replaced typically? No more than...what do you think?

The labor is .8 of an hour which could be anywhere from $80.00 to $120.00 roughly, and the parts run $474.81 for original equipment brand to $100.00 for aftermarket, roughly so check with your local parts store because they offer different levels of quality and guarantee with their alternators.