We have a 1995 legacy wagon. The other day the battery died. Replaced it. Today I noticed after turning the car off that something was running....sounds like a fan.

 

Went inside and a few hours later went out and the "fan" was still running. I turned the car on for a few moments then turned it off but it was still running.

 

The sound is coming from the engine compartment on the passenger side, by the radiator.

 

Also, don't know if it's related, the ABS light has been coming on for about a week. It's not on everytime I start, about every other time.

Did you uhh...check to see if it's actually the fan? That would really help. Try to pinpoint it with some listening....