2004 Mercury Sable

Recently, I had to replace the ac compression clutch. Thought that fixed the problem. High idle and doesn't seem to have much power. I noticed it doesn't have much voltage. I was able to get the car home but when I went to leave the next day to go to the store, the car will crank but shuts off seconds later. I'm convinced the alternator has gone bad because I witnessed it happen before with an old friend. The mechanic is thinks that it could be the fuel pump and maybe even the computer.