That's really strange. The only upgrade you need to win is the Speedmotor Engine, but it's impossible to reach the races without having it installed.

The only other thing that can really 'help' are boost capsules. You should be able to get some from shooting the floating boxes around the lighthouse ocean area. As far as I know, when you get the Beluga spaceship later in the game, blasting the boxes from the sky yields disproportionally more boost capsules, making the races even less difficult.

There aren't many general tips to offer for winning the races. Shoot like a madman only immediately after the race starts, but rather concentrate on overtaking opponents instead of shooting them up while racing for top position. Try to hit all the speed bumps if you can, and don't bump into anything obviously.

And of course keep space pressed down at all times! :)