Sale of a new house

No recapture or gain on the demolished building because you got nothing for it. Add the demo costs to the purchase price or construction costs of your new house and that's your basis. If the new house is a rental you have recapture on that. 

It may be best explained by example.  You bought the original house and lot for $50,000. Depreciated $25,000. You spent $100,000 demolishing the old house and building the new one. You sold it for $200,000.

Your cost basis is $100,000 + $50,000 - $25,000 = $125,000.  You have a capital gain of $75,000 ($200,000 - $125,000 = $75,000), of which $25,000 is depreciation recapture (section 1250 gain). 

In TurboTax (TT), I think it goes smoother if you report it as the sale of a business asset (Business items section of income), rather than reporting it in the rental income section.  You enter $150,000 cost basis and $25,000 depreciation claimed. 

Edited per martinmarks comment

ALTERNATE METHOD

The depreciation recapture can be avoided.  Here's a revised example. Although the net capital gain calculation is the same ($75K), depreciation recapture (which is taxed at a higher rate than long term capital gains) is avoided.

You bought the original house and lot for $50,000 and broke down the cost as $25,000 for land and $25,000 for building. You fully depreciated the building $25,000. You spent $100,000 demolishing the old house and building the new one. You sold it for $200,000.

Your report the disposal of the original building as a sale for $0. $0 sale amount -$25K cost basis + $25k depreciation recapture = $0 capital gain.

Your cost basis for the new building is $100,000 + $25,000 for land = $125,000.  You have a capital gain of $75,000 ($200,000 - $125,000 = $75,000).

In TurboTax (TT), I think it goes smoother if you report it as the sales of  business assets (Business items section of income), rather than reporting it in the rental income section.  You enter the disposal of the original building as a separate asset (property) sale from the new building with land.

While the explanations given are correct, they don't tell you how to deal with it in the TurboTax program. In order to give you those details, we need to know the following.

1) Was the last occupant to vacate the old house a paying tenant?

2) If yes to 1), when did they move out?

3) When was the structure demolished?

4) When was construction of the new structure completed?

5) What is the status of the new structure? Is it a rental? Did you sell it? Did you move into it as your primary residence? When?