Can a starter keep the altenater from working?

No! not usually, they are on separate circuits - however; some vehicles feed the power lead to the starter motor from the battery positive via the alternator, so best guess is that you may find the problem could be the connections at the back of the alternator.

Without any other reference to go on like the vehicle type and year etc it is virtually impossible to conclude where the fault (whatever it is!) might be!

More info is required!