The only way to know for sure is to meet with a lender. Having saved $10,000 is a great start. I've met with folks with bad credit and even bankruptcy to explore the possibilities. If we aren't able to buy now, we create a plan to improve the credit faster and prepare for when we can get financing approved. I can refer you to someone in El Centro if you don't already have someone in mind.
Some say 580 can but many disagree. Below 580 does not seem able to get credit at all for a mortgage.
It is not over. You need to do some credit repair. Bring your score up and buying could be possible. The blog below gives some helpful ideas to get on your way. Talking to a local lender may also help as many of them help people to repair their credit by showing some of the right (and wrong) things to do.