20 year old Teledyne Laars pool heater started making a "buzzing" sound when nothing is running

SOURCE: Hello

http://www.parts4heating.com/Pool-Heaters-Teledyne-Laars-parts-s/38.htm

SOURCE: starting a teledyne laars heater

check for proper millivolt reading( 400-600).it could be 20 different problems and/or components

SOURCE: My teledyne laars pool heater will not cycle on. The pilot is lit and the valave is in the on position

check millivolt output should be 400-600.if less than that you dont have enough voltage to power valve

SOURCE: Laars Teledyne Pool heater flames on for 2 seconds, shuts off

You have no flame rectification.....LLD series heaters check for a signal through the flame to ground; if the module does not detect this signal, it go through two more trials for ignition and then lock out the module. There should be a flame rod and it may need cleaning. I use steel wool.

SOURCE: Teledyne Laars LD250 Propane Pool heater cycles on and back off

Do you replace the thermopile or check the milivolts?
Check the Pressure gas
You need replace all of them terminals and check again the milivolts at the gas valve