From your screenshots, it appears you're receiving a few Main Board errors
at boot. I'm not sure if you guys are aware, but the Rainbow's startup tests are quite particular about timing. The tests expect a cycle-perfect 8088, and they fail if they encounter anything else. A good example is replacing the CPU with an NEC V20, a pin-compatible chip with the 8088. The V20, though, is slightly faster, and it leads to some serious failures when booting. Therefore, some ROM modifications are necessary to get the chip to work. Have a look at:ftp://ftp.update.uu.se/pub/rainbow/doc/v20prom.txt
While this isn't exactly the same scenario, it provides an example of the pickiness of the Rainbow tests. Additionally, talking with my father (one of the Rainbow's engineers), he pointed out that there are a significant number of "no-ops in the ROM to account for timing issues during self-tests." I'm not sure how accurate the 8088 emulation in MESS/MAME is, but it might lead to issues on the Rainbow.