Without knowing the exact condition of the house it is hard to give you too much info here, but it is unlikely that a bank would finance the house as an SFR without any kitchen or bath as it would not meet standards of occupancy. If this is a half done permitted remodel, all of the inspections would need to be signed off and all outstanding liens released before you could get conventional financing.
My gut feeling is that you would have very little luck getting a bank to lend using raw land as collateral today. People are dumping options on land left and right. If they would entertain land as collateral, you would likely have to tie up raw land value well in excess of what you are looking to borrow. No cash needed but terrible rates.
The construction loan is an option but you would need to go to the bank with full docs, i.e. purchase price info, competing bids from contractors to do the work necessary to fix the house, and an appraial of value when done. And they are going to want you to bring 25% cash to the table minimum. Cash needed probably 75-100K
IF it was me and I really wanted the house… speaking totally hypothetically here… I would buy a 6 month option to purchase the house at my price, pay the current mortgage myself during the option period, get a contractor in to hammer the place back together out of pocket, then go finance the place as an SFR at the option price. This all revolves around the house not being under water. If this is a short sale all bets are off as once you fix the house you have improved the house to the point that they may not want to let it go so cheap.
If it is under water your best bet would be to wait for the forclosure then approach the bank with an offer that they finance the construction loan as a mini-perm that would roll into permanent financing afetr repairs are made. They will be much more apt to work with you to get it off their books. I have seen several of these around listed as cash only with POSSIBLE financing through the bank that holds the REO.
