In the state of Texas, do we have to pay taxes on property that was sold under market value. The property is selling for $200,000.

What were the conditions of it selling "under market" ?

That can make a difference in the answer received.

The property has run down over the years and we do not have the money to have all the repairs done. We would just like to sell the property as is. We do not live close to where the property is located.

Assuming that this property has not been your principle residence, and also you have not ever rented it out...

You may owe capital gain on the property, but only if the selling price is higher than your cost basis. Your cost basis is the fair market value of the property as of the date of death of the decedant (i.e. its value when you inherited it) plus the cost of any capital improvements you may have made since then. If the selling price is greater than your cost basis, you include the sale as a long term capital gain on Schedule D of your federal tax return. If the selling price is below your cost basis then you do not report it (you can not claim it as a loss since you can't claim losses on the sale of personal property). Note all that's important here is the selling price and your cost basis - the fact that you are selling now "under market value" is not material.