Always hook the amp up to power and ground first, hook up the remote wire, and see if it powers on normally. Then hook up the speakers. In your case, I would disconnect the speaker wires from the amp, and check to see if the amp status changes. If it does, check the resistance of the speakers where the wires were connected to the amp to see if you made a wiring mistake and have a short or a unacceptably low impedance load.

If the amp is still going into protect mode with proper power and ground (and no speakers connected), it's probably time to call up and get an RMA to send the amp back. It's not unheard of for amps to fail out of the box. It's rare, but it happens. Whatever you do, make absolutely sure you have a correct speaker configuration before you try another amp though. If you accidentally damaged the first amp, you could instantly do the same to a second one.

Just to elaborate, take the fuse out of the fuse holder, and check the resistance. It should be almost zero.

Checking current through a fuse when it's in the fuse holder won't necessarily tell you anything. If the amp is in protect mode, or not properly turning on, it could/should draw very little current. Taking a current measurement therefore won't really tell you anything about the health of the fuse.

Usually a disconnected remote wire won't trigger a protection light, else the protection light would be on whenever the head unit is turned off.