Water – Why is noise coming from our hot water radiator even when it is off

I believe that means that the drain pipe of that last radiator is blocked in some way (or simply not or incorrectly connected)

for the connection you'll need to ensure the inlet and outlets are connected to the proper pipes

if it is properly connected then this can be an airlock to fix this close all other radiators and turn on the pump this will increase the pressure before the air bubble and might clear it.

if this doesn't fix it you'll need to check the drain pipes and replace as necessary.

Do you know for sure that this is a hot water system? Sometimes steam can sound like running water. If it is hot water, there is a giant air bubble in the radiator preventing it from filling. It needs to be bled off by opening the small valve near the top at one end. You will typically need some sort of tool or key for this. Slowly open the valve. Along with the air, hot water will spit out, so be careful. When there's only water coming out you're done.

If it is a steam system, there is an automatic air vent valve on one side or the other about half way up, it looks vaguely like a small bell. It's clogged up for some reason, preventing air from being vented, meaning steam cannot enter the radiator. It either needs to be unclogged or replaced.