The hot water for my roman tub faucet (for a tub deck) doesn't work. Turning the handle releases a small amount of water, but only for a short moment. I knew this was a problem when I bought the condo, but just never got around to repairing it. Now I want to see if I can fix it. My question:

1. What could be the issue, and how can I diagnose what might be the problem? My uninformed guess is that there is calcium build-up restricting flow in the hot water valve. If so, would that require replacing that valve or the whole faucet? The faucet is a Moen product-- how would I go about determining what parts need to be ordered?
2. Depending on the problem, is the repair one that can be done by a homeowner with little knowledge about plumbing?

The faucet is a 3-piece faucet. It kind of looks like this:

The hot water for my roman tub faucet (for a tub deck) doesn't work. Turning the handle releases a small amount of water, but only for a short moment. I knew this was a problem when I bought the condo, but just never got around to repairing it. Now I want to see if I can fix it. My question:

1. What could be the issue, and how can I diagnose what might be the problem? My uninformed guess is that there is calcium build-up restricting flow in the hot water valve. If so, would that require replacing that valve or the whole faucet? The faucet is a Moen product-- how would I go about determining what parts need to be ordered?
2. Depending on the problem, is the repair one that can be done by a homeowner with little knowledge about plumbing?

The faucet is a 3-piece faucet. It kind of looks like this:

Update: I installed a new cartridge this weekend, which did not resolve the issue. However, after turning the water back on, a handful of the sinks in the house released black sediment of some sort, and one of the lavatory sinks (in the same bathroom as the roman tub) no longer works (no hot or cold water). This seems like a very random effect of changing the tub's cartridge.