Beeping on diode mode and no resistance on Ohms measure.
A full wave bridge rectifier consists of 4 diodes.
Transformers which use centre tap use only 2 diodes for full wave.
First, verify your red and black leads are the correct way around in the meter by testing on a known good diode ( say for instance a common 1N4004)
Assuming a digital meter set to diode test.......red lead to the anode, black to cathode ....circuit of perhaps 0.4 (actually it's voltage drop but anyhow)
Reverse should show open circuit.
Measuring on low ohm scale will verify a short and it will be in both directions.
Note once again, circuit components other than the device under test can give incorrect and misleading results.
Now move to the bridge out of circuit in most instances........there are four diodes as above,
All point from the negative output to the positive output
Test each individual diode in turn, first say start at the top, test first on the left from negative (anode-red) to AC terminal (cathode) that is forward and expect somewhere around 0.4 on diode test range. Reverse should be open.
Continue for remainder, so next is red meter lead on top AC, black on Pos etc. etc.
One thing seems you are jumping the gun and determined to find a fault on the board somewhere before you verify the main transformer is working as it should.