Voltage isn't the only factor of a good battery. If you have a dead or dying cell, voltage could be in the OK range, but when you start cranking or asking it to do it's job, that demand causes the bad cell to basically drop off line and the power isn't available to do what it should. Only way to really tell is to put it under a load and see what it does, preferably with a load tester.
That being said, IF the other battery you used is a known good asset with the same or better load rating, then you kinda checked that box.
When you checked your fuses / relays, did you inspect the sockets for any corrosion or loose contacts? When checking, try pushing down/in on the contacts as sometimes they get loose in the holder, when the blades of the fuse or relay press on them while being plugged in, they can pop out the back and cause loose connections. Also some fuses have been known to get hot and slightly melt the fuse holder basically causing the issue I discussed above as well.
Inspect grounds for loose connections/corrosion. Inspect wire harnesses, especially in the areas where you were most recently working. There have been some who have experienced corrosion in the harnesses, especially at any splice points.
