Hi,
The LED usually shows output voltage (please check). If so, then the switcher starts and stops continously.
Then I assume the "switching circuit" (IC, transistor, diode) is working.
How old is the power supply?
A defective capacitor may cause such behaviour.
Are all the capacitor tops flat (not "blown" outside)
Do you see any signs like floid, oil, smoke .. at the PCB underneath the capacitors.
One possible reason may be a defective feedback path.
Klaus