EDIT: Previously I reported that my saw was tripping the breaker for a different circuit, but I was mistaken. I'm updating the question with the correct information.
I have a pretty old Craftsman 10" table saw. At my previous place, it would trip the breaker or GFCI for the 15a garage circuit but ran fine on a separate 20a circuit that happened to be in installed in the garage. I'm not sure I remember correctly, but I think there was no GFCI on that 20a circuit.
Now I'm in a new house, and there's no 20a circuit in the garage. I have two 15a GFCI circuits in the garage. On one of them, when I try to power up the saw, it doesn't start at all (no relay click, no motor hum, nothing). On the other circuit, it trips the circuit breaker immediately. I didn't hear the saw's starter relay click there either.
Trying to diagnose the issue, I did get the motor running for a few seconds when the saw (with blade removed) was upside down. I didn't realize until later that it's a no-no to run this saw upside down, because the start relay is gravity based and just closes when it's upside down. This means I was running the motor (with no load) for a bit with the start relay completely closed. I hope I haven't damaged the motor!
As a next step, I disassembled the switch circuit to check it out, and the overload, relay, and switch seem to be fine. I put in a new capacitor just in case. Still no joy.
So, my questions are
Since the motor ran when I inadvertently closed the relay by turning the saw upside down, it seems one problem is that the relay isn't getting enough juice to turn on. The spec sheet says it triggers in the range 25-30 amps. I infer that the saw is trying to get its startup juice but isn't getting enough to trigger the start relay. Is there a solution to this problem? My understanding is that all AC motors take extra juice to start up, and breakers are supposed to tolerate that temporary increase.
The start relay may be bad, as I only tested continuity and don't have equipment/knowledge to test that it activates properly. It's a Klixon 3CR 25-30 amp that is not made by the manufacturer anymore though I did see it online at one seller for $40. Is there an easy way for a DIYer to test it?
Is there any reason why the saw trips the breaker on one circuit but does absolutely nothing on a different circuit, both 15a?
I suppose that the fact that the saw trips one of my 15a breakers proves that it's trying to draw too much current at startup, as suggested by @DrMoishe Pippik. Indeed, the starter relay needs 30a to close if I understand the spec sheet correctly. But I'm really stumped to explain all the observed behavior!
Any further advice/help would be greatly appreciated!