Upon arriving home, the car shook then stopped running. Tryed to start it, but no go. Upon trying to start it, the car would turn over putter, then stall. Under the dash board there's a pannel which a buzzing sound was coming from. I checked it and it was coming from the top right relay and it was also vibrating. Need help.

SOURCE: no flashers or turn signals

see if power is going through the switch

SOURCE: no flashers or turn signals

Try the fuse/breaker panel under hood, drivers side.

SOURCE: My 05 Corolla stop running.

Sounds like you need a fuel pump. The first indication of a fuel pump issue is a hum or drone noise.

SOURCE: 2003 toyota avalon gets check engine light and goes when idleing

Take the car to a local Auto Parts Retailer, and have them check the fault codes on your on-board computer. Given the year of your car, it is probably an OBD-2 type computer. They can print out whatever the computer diagnostic says the problem is. I am going to guess the throttle position sensor is to blame since it sounds just like what my sister's Mazda Mommyvan was doing.

SOURCE: Gurgle sound under driver side dash

It sounds like you may have a small air leak in your cooling system that is trapping air, and you can hear it gurgling through your heater core. I would keep an eye on your coolant level, and also you can rent a pressure tester from Auto Zone that you can hook up to your overflow tank and test your system for leaks. Most likely you will be able to tell where its leaking from, or see if its holding pressure like it's supposed to. Just follow the procedure closely and don't overpressurize the system.