Umm... unless "stealing an electric wheelchair from an old person" is an option for you, I really don't see how you're going to build a go-kart with a pile of wood, twenty dollars, and no metal...

I need to build a go kart.

You "need" a go kart, what is the mafia gonna whack ya if you don't have one?  

I don't want to offence, sorry

I too have just finished making a motorised go kart though i had a budget of £50 dont know what that is in dollars, but i just used two old lawnmower engines (the same of course) and aluminium and a welding gun(dont know how to spell it in american!)to make the frame! oh and i used whellbarrow whells for the tyres. You should just go and have a luck down the neerest scrapyard!

I don't want to offence, sorry

I said I'm sorry!   

Sugestions:

Go to a dump or recycling center and pick up a junked lawn mower, the engine might be strong enoughn to et you going depending on your size and weight. (and the tires might be helpful.)

While you're there ask about for junked bikes, (good for wheels and chain and the frame can be hacksawed into a partial roll cage)

A junkyard would also have some nice junk like an old car seat and steering wheel.

Depending on your age (I'm guessing teens) they'll prolly let you just have the stuff, or be willing to trade you what you want in return for a few hours of work claaing up around around the place.