An alternator won't do you any good until it's running, what I'd do is get a battery, not a cheapo, make sure it has the required amps . . . once it's started you can take your alternator to most parts stores, and they can check it for ou if you don't know how to check it or don't have the tools . . . your battery won't go dead just driving it to the parts store . . . also check to make sure you don't have something left on that could drain the battery.

Edit to add:

If your "new" battery went dead in 4 months, take it back to where you got it from . . . they should give you another one or your $ back!