C113 is indeed populated. Its ceramic, like others, so I can not say the value. Apple seems to stick to a common group though on boards.  So it may be like others such as C118. It does look like the pads are gone. Scratch the material to verify if its copper. Usually when pads are gone the substrate is more of a tan color. Those look darker. The only good thing is that I dont see traces from it, just two via. If so, one could glue a cap in place then use small wire to reach the vias. Would not have to even be covered wire.

I pulled the cache, it still booted without it. So in your case, make sure the ROM and cache are empty. At least you can rule them out.

I would also try just one DIMM slot at a time, which I think you did.

If you are getting a green light, I think your power supply is fine.

Also for the record, and verification, mine did boot with no battery. Which I now pulled and will toss after seeing this