There is a program available for people with bad credit to be able to purchase homes as long as they can afford the mortgage. They do require you to take a free class online in order to qualify. I am a certified agent through this program, please let me know if you would like further details.
You may be able to get a loan (particularly with the big down payment) but who knows what the rate would be. The only way to find out is to apply for the loan, pay the $17 for the credit report, and then the lender can give you an accurate quote.