96 Tahoe Randomly not starting

[CalebD]

Ok I have a 96 Tahoe 5.7 with 113k miles. Last week it started doing this weird thing where I'll turn the key and all I hear is a load buzz. Engine doesn't even attempt to turn over. If I just keep the key in the on position and try starting it a few times it just keeps buzzing, but if I turn the key all the way off and then try again it'll fire up like it was brand new. Right now it's just annoying as it never takes more that two tries to get it started, but common sense tells me whatever is wrong will eventually leave me stranded somewhere, so I would like to get it fixed sooner than later, any ideas as to what could cause this?

 

[lesterl]

If the engine isnt cranking suspect starter or starter relay (I just got stranded at gas station yesterday and had to install a new starter (I have 287k tho...))