Loud rumbling/buzzing for 10-15 seconds and then power goes off

What exactly is this 'loud noise'? Is it a constant grinding or rumble sound that changes with drum speed or is is an occasional thumping, banging noise as the drum speeds up or slows down? A grinding or rumble is often a drum bearing and Thumping is commonly the 'suspension' the drum rides in to stop it 'walking across the room or shaking itself to pieces as it goes into high spin speeds. Your machine's age will only affect you if it is a very old machine and parts are difficult to find.

Try plugging another sound source into the unit. The buzz MAY be pickup of magnetic fields in your guitar pickup that clobber your notes from the strings. Bad guitar cables are another possibility. By putting clean music from say a CD player into the unit you can find where the source is. If the CD player generates the same noises, then likely you have a failure of filter caps in the amp or other component failures. Also make sure your guitar can't "hear" the amp as feedback can do strange things.

check brake fluid level.

master cylinder might be of interest, but i would check the fluid level first

It sound like you may have sound processor problem which is part of the main board, I would also look at the 12vdc from power supply to make sure it is clean DC.
Parts: http://www.shopjimmy.com/catalogsearch/result/?q=l37hdtv10a

http://en.wikipedia.org/wiki/Capacitor_plague

You have a Genesis 1. Make sure that you are using the correct power supply; the first models use a different voltage than the second or third models.

Color wheel needs replacement

what is the model #

sorry cant solve it ,i called all the loewe service agents and they all said the same thing, put up with it. a new engine/colour wheel cost around $2500,

Sounds like the fan is hitting some ice build-up. If you can access the area of the fan motor you can try a hair dryer to defrost the ice out of it.

Is the buzzing coming from the back of the TV, staying loud even when the volume is turned all the way down, or is it coming from the speakers?