I recommend 5V 1uF memory capacitors, that's what I used on mine. Never worry about batteries, leakage and very inexpensive. All you have to do is play a game once a month.

For the most part, the game should play normally without a battery. The battery just holds the audit and adjustment information in memory. Just be aware of the following:
> you might experience some oddities such as no voice sounds if these adjustments are not set because of the absence of a battery. Once you set them to a proper valid setting they will work
> On some 6803 games you might find you cannot get a credit into the game if the memory becomes corrupt from a bad battery. Go into the audits and adjustments menu, set the credits-per-play to a valid number.

Never hurts to double check the logic supply, make sure within a few tenths of 5VDC and check AC ripple, you're probably ok - at least you know the processor is running a program from the flashes. I'd also say swap that CMOS ram out next if you can't boot it.

Rectifying AC to make it DC results in a pulsing DC output. Filtering "fills in" the gaps between the pulses. If viewed on a scope, the rectified DC is never pure like the DC from a battery. It has waves that ride on the DC - ripple.
Logic circuits don't play well when the ripple is too large. You can measure a good DC voltage and still have a crappy DC supply because of the AC component. Measure
the DC supply using an AC setting on s DMM if you don't have a scope. In general you want to measue less than about 500mvAC of ripple. When is too high, that's usually because of a filter cap problem.