Can I purchase another primary residence while delinquent on investment property?

I have a primary residence that I am current on and have never been late on. The property has appreciated significantly in the two years since I've built it. I also have a rental property that hasn't had renters in it for a year, and no payments have been made during this time frame. I would like to sell my primary residence and buy another property. My rental property needs repairs in order to rent it out. I have been declined for a home modification for this property, and I have been trying to short sale the house for over a year now. I have had someone willing to purchase the home, but the mortgage company has not approved it, and twice I have lost potential investors that are willing to buy the property for less than 10K of the balance that I owe on the home. Should I try to sell my current home and take some of that money and bridge the gap between the short sale difference. If I do that how soon could I qualify for a new primary mortgage. All other bills are paid on time, and my score is not too terrible considering I haven't made a payment on the investment property in over a year. Should I try to make the repairs and rent out the property again, or should I try to continue to short sale the house or sell my primary residence to get the extra cash to cover the difference on the investment property.

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