I had a look at the SYM-1 Reference Manual
* page 37 (page 4-15) shows the memory system
* page 49 (page 4-27) shows the jumpers
* page 52 (page 4-30) describes jumper usage for rom sizes
* page 53 (page 4-31) describes jumper usage for rom placement
U21 is connected to signals S11, S12, S13 which connect to jumpers B, F, K. B1 F4 gets you A11 and A12 on pins 18 and 21. S13 is \CS, jumping to K-11 and K12, K13, K14 (wire-OR) should put an 8k ROM at C000.
All that confirms what you did: so perhaps it is worth checking the ROM. Is the machine able to run the monitor so you can read out some of the ROM content, or does it completely fail to do anything with the ROM installed?