None of those are even close. A 7408 is a quad AND gate. The 7402 is a NOR gate, the 7404 is a hex inverter, and the 4050 is a hex buffer. You'll have to order the correct part.

When using a TTL gate to turn on a transistor (like WMS solenoid circuits), you have to use one that can handle some current.

74F08 is what I would use as a still easy to find replacement.

When Replacing 74LS parts you can use 74HCT.

Only use 74HC when you are replacing another 74HC

A 7402 and 7408 are certainly NOT interchangable. The input and output pins aren't even the same. Has the board EVER worked? If not, I would suspect that someone before you replaced it (and maybe both of them) with the wrong part. I tried looking at pics of a Data East board on Pinwiki, but the resolution is not high enough to read the part number off those chips. You should definitely verify before doing board work.

Both the schematic and assembly drawing say those chips should be 7402. I'd still like to see 7402 on a board, but I think your board has the wrong parts on it.

1-Fullscreen capture 10282016 24823 PM (resized).jpg

Both of those ICs in the pics look to have been replaced, based upon the appearance of the solder connections.

bttf here with 7402

bttf 7402.jpg