Yeah you have power problems. Common for all WMS games after this long.
Grab the manual:
http://arcarc.xmission.com/PDF_Arcade_Williams/Sinistar_Instruction_Manual_(16-3004-101)_Feb_1983.pdfAnd the schematics/drawing set:
http://arcarc.xmission.com/PDF_Arcade_Williams/Sinistar_Drawing_Set_(16P-3004-103_Feb_1983).pdf So you're a bit familiar with the hardware.
Get a multi-meter, and start probing the power lines and check your 5v line coming out of the PS board (RJ2).
Your PS board can use a rebuild, seeing that you still have all the original caps and components on there.
If you're somewhat familiar with a soldering iron, this'll be a cake-walk...if not, you might want to get someone to rebuild it for you. Dokert and YellowDog at KLOV are Williams experts.
If you're a DIY guy, get yourself the WMS Power Supply Deluxe Rebuild kit from
bobroberts. I'd "shotgun it" and replaced all the caps, the regulating IC's + sockets, the Bridge Rectifier....etc, with new ones. Also flip the PS board over and check for any damage, or cold-sockets (solder points with cracks, or holes in them) and either replace the connection headers or re-flow the cold-joints. Probably best to just replace them with new ones. The Connectors to those headers could probably use a replacing too.
Also check and re-flow the solder on the Fuse holders too, and be sure to squeeze the clamps so they make absolute contact with the fuses.
Williams boards are very finicky when it comes to power voltage, but the best thing you can do is get that original PS Board nice and healthy first...that'll probably fix most of the issues, if not all...