(Apologies for double post but wanted this separate)
EDIT: [Also I read that you're an engineer so this is probably a little 'dumbed down' for you actually, LOL, but I figured best to explain it in simplest terms possible!]
Also, another key fix that you should check is those edge connectors and the edges on the boards! FIRST, what I do is - take pictures of all the edge connectors (like the little plastic Molex ones etc) going to the board! Most of them are double-sided and if you put it in backward you fry your board! So take a good picture and mark one side with "COMPONENTS" or something on the plastic of the edge connector so you know which way they go back in. I use my phone to take a ton of high-res pics of each edge connector, even if I've done it 10000x (like with my Space Invaders), before disconnecting everything. Even if I have the pinouts memorized, because it's a good habit to have.
For most games the edges and edge connectors are the source of the majority of the problems. When you pull the board, grab a regular ol' pink pencil eraser and erase (don't scrub too hard) the edge of the PCB (where the fingers make the little traces where the connectors go in). Just erase it like you're cleaning off the crap that's accumulated. If you can, get some DeOxit or other contact cleaner and give the inside pins on the plastic edge connector a slight blast, then follow up with canned air so it dries out completely. Check the pins on the edge connectors to make sure none are bent, broken, and give the wires a slight tug (not too hard) to see if any are loose. If they're loose, you'll have to replace that pin, which is pretty simple to do.
Check the edges on the boards where they meet the connectors (they'll be dual-sided so check both sides). Is there solder popping up, or traces broken? If so, there's your problem, and you'll have to either reflow solder or buy a fingerboard and repair it that way (I think for Pac-Man there's one called PAC-FIX or something like that). If there isn't, reseat them, you should feel them 'grabbing' the board a bit so there should be some resistance. Flip her on and try her out and see if that helps a bit.
IIRC, on Pac there's also a test mode switch. Someone you could ask would be @save2600, he's well versed in this stuff and I know he's done a ton of work on Pac. If it's a clone it's probably got similar problems.
When the game dies, does it play blind? Like can you hear the sounds and the game still playing, but the monitor is out? It sounds from your post it doesn't, so that possibly rules out a monitor problem. The first thing I learned about arcade game repair is this:
"Arcade games seem complex but they're really just 3 things: 1) Power Supply, 2) Logic Boards, 3) Monitor. All repair will center on those three things, so if you can eliminate 2 of those three, you'll be a long way to fixing things."