the reason for your board not powering on is most likely being caused by a faulty power supply. there might be some life left in it, however, and I don't expect you to perform this task immediately (it takes some time and understanding for those that aren't like technologically-inclined) but allow me to explain some fundamentals of how these work.
the power supply, contrary to what most newbies believe, doesn't power anything that's AC driven unless it's a very messed up arrangement.

AC powered items are 1) the power supply itself 2) the monitor and 3) the marquee light fixture.
the power supply outputs a series of different sized voltages, in the case of MK3 those are +5, +12, and -5. only one of these voltages, however, is what's called "regulated". the most important voltage in any video game is the +5, because that's what's required to "power" the video game board. although it's called +5, that doesn't mean that it's exactly 5.00 volts, in fact, the voltage needs to be a little bit higher than 5.00, more in the realm of 5.10, in order to ensure proper operation. you can actually declare this voltage through the +5 adjustment on the power supply, but it's not something you just turn and hope for the best.
to do this, you need a digital multimeter, which is capable of measuring this voltage so that you get an accurate reading of what your +5 is set at. over time with power supplies that have age and mileage riding on them, this adjustment for lack of a better way of describing it goes OUT OF adjustment. if the power supply still has some life in it, you can adjust this back up to the desired 5.10 volts. otherwise, there are some power supplies that will either be incapable of outputting that high of voltage anymore, or there are some that are just seriously broken.
the power supply that was in my Killer Instinct cab would sometimes go into overload protection mode, which essentially shuts the power supply down, despite having electricity going to it. no degree of adjustment could fix this, I had to replace the unit. that particular one was of the "screw terminal" variety, which means that you attach all the wiring for the different types of voltages to terminals held down with screws.
if you look at your game board, you will find a large black wiring harness plugged into it, and this is called a JAMMA harness. JAMMA was just the name of the wiring standard (because many classic games by different manufacturers used their own wiring pinouts, which meant that swapping games often required a full stripping of all wiring from the game cabinet and replaced with new wiring mated to the new game's board). there are certain pin locations on the JAMMA edge of game boards that take these different voltages, and the wires attached to these pins on the JAMMA harness are what run to the power supply.
there's another kind of power supply that resembles that of a PC XT power supply that has a white block "molex" connector that runs to the JAMMA harness, which makes a direct power supply swap very easy, but I can't tell you what kind of power supply you have, cause I don't know what type of power block Midway put in MK3.
I would say minimize the confusion and just replace the power supply with a new one, but a point to consider is that most new power supplies are adjusted at the +5 setting for 5.00 volts exactly, or for all intents and purposes, you don't know what kind of voltage it's going to be set at either.
switching power supplies, like the kind I'm talking about, only really work unless there's a "load" present, meaning that a game or some other device that requires power needs to be attached or else it won't function properly. the other voltages I've mentioned, like the +12 and the -5, unlike the +5, are merely products of the switching process that the power supply performs, and are also not regulated. it's not uncommon to get readings with a meter on these power rails in the realm of 13.85 volts and -4.89 volts respectively, because these don't really matter all that much, they really only power the sound hardware/amplifier on the MK3 board. it's worth noting that if the power supply is in bad enough condition that it no longer creates +12 and/or -5, you will not have working sound in your game.
however, despite requiring a load, it is perfectly safe to get a rough idea reading of where your +5 voltage is at prior to hooking up your JAMMA harness back to the game board for roughly 10-15 seconds without damaging the power supply. the best part is this reading comes up almost instantaneous and should either give you enough time to make the necessary adjustment or maybe you even have it at a good spot already. anywhere between 5.00 and 5.20 is acceptable here, then with your game plugged in, you can fine tune it. pay mention that your "rough idea reading" can be done at either the +5 and ground terminals on your screw terminal power supply or you can plug the meter probes into the red and black wire holes on a molex type. your final reading should be at the +5 and ground wires on the JAMMA harness (also red for +5 and black for ground) ... this takes a little bit of finesse, because you don't want to slip and start running your meter probes along components that carry electrical current.
I hope this gives you a better understanding of the power supply and how and why all of these things work.
as for the greenish tint on your monitor, this could be caused by any number of reasons.
the good news (I think?) however is that if your UMK3 board isn't powering on, you will not see a faulty video signal coming from the board that's a solid green. the bad news is that narrowing down the cause of the monitor problem not only requires that you resolve what's most likely a power issue first (as I mentioned previously, this might just require a +5 adjustment and not cost you any money at all!). the green tint can either be a maligned adjustment of the green drive/green bias controls on the monitor neckboard (more finesse) or worse yet could be a damaged monitor tube.
I won't give you monitors 101, I'm sure someone else can describe it better and maybe not write a novel doing it.
good luck, and welcome to KLOV.