Quoted from DakotaMike:

Yeah, I mean a totally completely dead game could just be a blown line fuse by the power switch. Easy and quick to change, and that could get you more info. I think they're usually an 8a slow blo.
Otherwise, the power supply could be totally fried. But I'd be doubtful that it would be totally gone to the point where nothing lights up or happens on a power-up. If it is just the line fuse, then that's a very quick, easy and cheap fix.
Even power supply boards aren't too expensive in the grand scheme, at least for most games. But you can't really diagnose much when the game is totally dead like that. Short of just checking fuses and looking for obvious damage.
Offer-wise, I say $1000 to $1500 is fair. I think Batman Forever's average-price is like $2500, so that gives you $1000+ of wiggle room in case you need to buy new boards or displays, and your time of course is worth something. And who knows might not be very much wrong with it. That's probably what I would do.

Quoted from Jediturtle:

I apologize that this may be a super obvious suggestion, but it appears as though you are new to the hobby, and the way you worded this makes me need to ask. Besides just connecting to power, you did turn on the power switch, right? No offense at all intended, but I have known of people not realizing (modern) machines have a switch.
Best of luck. From what can be seen in the pics it looks beautiful. It's a fun game...I'm surprised by some of the negative comments here as BF is usually regarded as one of the better Sega games. Hope it works out for you and is an easy fix!