Car Problem - Electric-ish - Exercise #327

[Jurollo]

Ok so I was driving my car the other night and the electricity started cutting in and out, turning my radio off and on in the process and my car seemed to hiccup as well when this happened, but continued to run. The digital temperature thing turned off as well. The next day I looked at the batteries and they were corroded but I cleaned the terminals and the car fired up. NowI got out last night and it won't start, no power. It gets sporadic electricity but doesn't have enough juice to start. It is a 1993 Ford Taurus SHO, good condition, has been serviced regularly. Could it be fuses? Should I look towards the battery again? Alternator? Thanks in advance.
~Justin