|A buzzing sound? Well electrical noises when starting are a specialty in themselves. If it was plain buzzing and it was closeby, its probably the ignition switch. If the buzzing is in the engine bay, its likely to be the starter engagement relay (the one just above the starter). Its not likely to be caused by the starter spinning on its own unless its bearings are wrecked as well. A third possibility is the starter relay thats plugged into the fuse/relay housing.
If its the ignition switch there's a simple tell tale:
- is there an unusual pause ( a second or more than you expect) before the starter kicks in? If so, change the switch.
- if there isnt a pause and it sounds like someone is playing some very small drumsticks - and very well - its the relay in the fusebox area.