Do not think it is the alternator, it could be several different things, the most common problem we have seen is the crank shaft position sensors failing. It could also be a ignition module or computer itself.
Are the things you mentioned very expensive to repair? Thanks.
crank sensor 1.3 hours labor part 70.00 ignition control module 213.00 parts 1.3 hours labor computer 170.00 parts .8 labor.