If I pulled an eprom off one of them can I identify the chip with my eprom programmer?
That's one way - for arcade games, you can use ROMIDENT to figure out what the ROM belongs to. It's really useful for arcade games, since all the ROM data has been archived thanks to MAME. Just read the ROM, run it through ROMIDENT, and *poof* - it tells you what it goes to. Try it, it's fun - pull a random ROM off any normal arcade board and read it in. It'll tell you what game, and what socket location (usually).
For computers, not so much, especially for weird obscure stuff. The ROMIDENT database only includes known patterns, so anything really off the wall (or some bootlegs), there won't be any entry. Most poker and trivia boards don't identify either.
For the obscure computer hardware, I usually dump the ROM and disassemble the code, you can see roughly what it's doing. Also, by tracing out the board, you can determine what it's capabilities are, thus allowing you to figure out what it would have been used for.
manufacture name on #2 boards is Identicon
That's not a manufacturer I'm familiar with either... Perhaps it was a custom thing, or some other obscure key-to-tape or other poorly documented/forgotten application. Hard to say without seeing it.
I love puzzles like this
-Ian