1) check the power
2) click on the test button as you power up the game
3) if you have a logic probe, check the clk pin on the 6502 processor and see if it's changing state
those are the first 3 thigns I'd check. When the test mode is set, The system boot up test code only requires 1 ROM to be working. and will first check the RAM check then check the ROMS and will beep if a RAM or ROM is bad. the test code is quite nice and clean and only requires
1) the CPU to be working (including clocking etc)
2) the address and data buses to work
3) The ROM code on the one ROM (dont' remember which) to be working at least to a certain point.
once that's working it immediately checks RAM, if RAM fails it beeps. once RAM passes it checks the ROMs and you can see stuff on the screen as well as beeps for failures.
additionally the two ROMS that stand by themselves are the graphics ROMS. you don't need them for testing since the system beeps on failures, but if they are not working you get all kinds of stuff like lines or solid color screen. I'd start with the first 3 tests before looking int that though.
By the way if you get beeps the beep codes are not necessarily correct. The odd numbers usually relate to the chip in the manual. The even numbers however can indicate a failure of the RAM in the manual or BOTH the RAM in the manual AND the previous RAM (or likely in that case one of the IC chips that interacts with both RAMS as each RAM chip only contains 4 of the 8 bits of any memory address of course) I learned this by reverse engineering the code after trying to troubleshoot a "bad RAM" that was not really a bad ram. and noticed that if two rams failed it gives you the "even" number of beeps, whereas you'd think youd first get the "odd" number of beeps, replace that, then the odd number of beeps.