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.
This is exactly what I’m talking about – financing that would allow purchase of the property with the repair costs. The repairs are the “construction” to which I was referring.
The lender would fund-control the repair costs to make sure the work got done and when it’s finished the property would conform to conventional lending criteria. At that point you could go to a conventional lender and get a long term loan on it.
And yes, there are a few lenders that might accept another property as additional collateral. Finding one that would take vacant land on might be tough right now due to market conditions, though.