Welcome to the forum!
What you are likely hearing is the internal circuit breaker tripping. The red light on the left should also light.

First, disconnect all wires to the transformer, and turn up one throttle at a time, from right to left they are A, B, C, D. The circuit breaker should not trip. If it does, there is either an internal short, or the circuit breaker may be defective.

If the transformer passes this test, hook the transformer terminals A-U to the track through a lockon. With no trains on the track, turn up the right throttle (A). The circuit breaker should not trip. If it does, there is a short in the wiring or the track.

If the transformer and track passes this test, put one locomotive on the track at a time and see if the circuit breaker trips. Try each car in turn and see if the breaker trips.

If there are no obvious shorts and the circuit breaker still trips, then the breaker may be weak and needs replacement.

I have a scan of the ZW instructions, but I cannot attach it due to the attachment size limit on this forum. Perhaps it can be e-mailed if you wish.

What is the model number of the transformer that stopped working?

Larry