You are asking whether you can enter the USA from Mexico without a valid visa or waiver? There are legions of freshly-minted border patrol officers in shiny new 4x4's just hoping you try....but in reality, they'll merely turn you back at the point of entry. You seem to be confused about the lack of controls when you exit the USA: this has no bearing on what will happen when you try to re-enter.
If you've still got a week or more left on your visa waiver, why not enter immediately and, at worst, over-stay? If you're caught, they'll make it uncomfortable (and forbid you entry in the future, if that's a consideration), but you might at least get to sell your bike.
But ideally, you ride to LA tomorrow and sell the bike in a hurry, then exit on time. That way you can come here again next time you become eligible for the waiver program---or apply for a visa. To the best of my understanding there are no extensions in the waiver program, but I'm prepared to be proven wrong about this.
Or: fix the radiator and carry on. How hard could that be?