When I bought my Judge Dredd I had the exact same problem with the test buttons not working, plus the coin accepters were dead and the start button. So I couldn't even play or test it. The previous owner left the batteries in and they leaked all over the MPU board. At least 35+ components were damaged. Now I can change a few resistors, diodes and transistors if I have to, but 35 was a little much for my skill level and time. Since I bought it via ebay and the seller had the auction as "working" I contacted him and we worked out a deal and ended up buying a new MPU board and I sent him the damaged one which we felt was fair.
So what I would do is get a new MPU or repair it first before working on anything else, because you can't test anything without it.
There's a few guys on the forums that repair boards this thread talks about a bunch of them
https://pinside.com/pinball/forum/topic/recomendation-for-board-repair-guy
If you just want to buy a new one http://www.arcadeshop.com/parts.htm seems to have the the best price for it. You just need to call to order it cause their web site doesn't have a shopping cart.
If the batteries leaked really bad you may need to change the connectors that go to the board too. This is something I needed to do.
https://www.greatplainselectronics.com/default.asp is your place for that
If you need a list of the connectors let me know cause I have it right next to me just need to type it out lol.