Trying to source a PCB component (a slow blow fuse I believe!)
You are correct, it is a fuse.

You could potentially replace it with another 10A/350V fuse. The problem with doing so is the timing of the fuse is not known, which could be a problem with inrush current. When I have found myself in this situation, and the inrush current is not known (because I was in a hurry), I started with fast blow fuses and worked my way to slow blow (but that was also with replaceable fuses). 

The best thing to do would be to find a BOM (Bill Of Materials, with all the parts and manufacturers listed on it) to find a direct replacement, if that can't be done, then experiment. 

Another note: The inconsistency in the circuit could still exist, so even if this is repaired the fuse might fail again.