Is it obligatory to fulfill a vow to fast for thirty days if the vow was conditional upon receiving a house from the state, but the state granted money with which a house was bought instead of giving the house directly?

You must fulfill the vow after acquiring the money from the state to buy the house, because there is no difference between owning the house or the money to buy it, unless you intended to own the house itself. In that case, you are not obligated to fulfill the vow if your intention is not realized, though this is unlikely.