You really didn't pay off your debt, you consolidated your debt and got (hopefully) a low or no interest loan. It may not show on your CR, but it does in your checkbook! You have not really substantially changed your situation, you have simply made it look that way to lenders who pull your CR.
I suggest you repay the loan to your folks, have some reserves and a good downpayment, then buy the house.
<EDIT: Pre-apologizing if below sounds like some guy telling you how to run your life, but that's kind of what it is. $0.02>
Couple of things to add.
1) Is there something in your situation where you need a mortgage asap?
2) What were the "tons of credit cards and loans with high balances?" Which ones are still
open? Which ones are you still using? <and this one is important> Which ones have balance increases since being paid off? Why?
#1 is important because preparing your credit/down payment/other debts can be a huge money saver in the long run. Not just a few hundred bucks either.
#2 is important because the spending habits that got you in debt hell (been there!) will get you back there in no time, especially with a mortgage payment. Landlords are much more forgiving of a late payment
Side note on the loan from the parents - this will probably come up, and likely be considered gift funds (otherwise, it's a loan and will count towards your back-end ratio). In that case, you'll need your folks to sign a paper saying it was a gift and you don't owe them anything.