How far from the sink can we install the dishwasher without major remodel?
There are no code regulations concerning the placement of a dish washer.  As AWMoore mentioned, you will need to supply a hot water feed and a drain, with a trap. You will have to see where you can tie the drain into the system being sure to meet the drop to run ratio. You can most certainly find a place to make this connection in a basement. To save head space in the basement , the trap can be installed above the floor behind the dishwasher, and the dishwasher drain hose install there, kinda like a washing machine.