Purchased a House with a Cash Offer and Conditions Have Been Met

If you walk away at anytime you will lose your earnest money you provided as well as if you can't perform the contract. As for legal consequences you should consult your lawyer.

You should get in contact with your real estate agent right away and let them know what is going on.  They maybe able to extend your closing date out some on the purchase of the new home. 

If the seller is not willing to extend the date you may be in jeopardy of losing your earnest money because you did not adhere to the terms of the orignal contract.

Like Steven sugested, you need to be consulting w/ a real estate attorney.  You said your purchase contract wasn't "conditional upon the sale of our house", but is your contract conditional upon you getting financing? (They could be two separate conditions) If so, an attorney should be able to help you, if you have to back out, or if the seller's try to back out (not giving an extension) and keep your down payment.