If it's a solid color screen it's probably suicided. I would recommend trying the Razoola CPS2 Suicide tester program rom to make sure. I have one cps2 board where even after writing keys to it, it stays on a blank screen. So using the Suicide Tester program rom will let you know if the error is just the keys aren't being written correctly or there's a further problem. One issue I have found with -3 and -4 CPS2 b boards is they sometimes require more 5v to program the keys... Can you test voltage at the jamma edge as well as on a chip and see where you're at? Should be 5v... if it's 4.8v at the chip that could be the problem.
Also, I would recommend practicing soldering on throw away boards a lot before ever doing a "production piece." So in the future if you need to solder something to through hole components, experiment on a throw away piece of tech first to get your method/temperature/process down.
There is not really a recommended rom reader/burner because it's all about what you need. If you only want to do CPS2 27C4096 type roms you can probably get away with a cheapy like the TL866II variants for around $50. If you want some slight future proofing you should look into the gq-4x4 for $100. If you really want to go big look at the BK burner or something else that is more pro. Eventually you might want to get something that does 48 pins.