Try a PRAM reset, which is the same method, even on a brand-new Mac.
Restart, while holding command-option-P and R. The command key would have a weird squiggle on the key, and an Apple icon.
You _should_ hear a boot chime sound. Even if you don't yet hear anything, continue to hold the same 4 keys. The chime should begin to sound, then repeat every few seconds while you continue to hold those keys.
The battery is the old standard Apple computer battery, and probably is dead. It's known as a 1/2 AA battery, 3.6 volt lithium battery. Take the top cover off the IIci, then release the latch for the power supply, and pull that power supply straight up out of the case. The battery holder is underneath that power supply.
Replace the battery. That, plus the PRAM reset should fix your video and sound issues.
- btw, you can easily find Apple's service manual. It shares info about the IIci, the IIcx, and also the Quadra 700, which all use the same case. Just google for Mac IIci service manual, and you should get several links.