All other drains including sewer drains great. House built in 1985. Drain is made of PVC pipe. This basement drain is not related to kitchen or laundry.
We put a snake in (by hand) and it would only go about 2 feet before it hit something.
If we use a power auger is there any chance of damaging the PVC pipe? How do we know if there is a trap or a bend in the pipe? It seems to be one of the two last drains before it leaves the house. The other drain is a plumb in and has never been used. Is there any chance house settling could have damaged the pipe? We don't want to create a bigger issue.

How do we know if there is a trap

There will be (has to be) a trap.

If you met resistance at 2 feet you were probably hitting the turn out of the top of the trap. It can be difficult to get past it with a manual snake because you pushing down on the snake which has made a 180 degree turn up and now trying to turn another 90 degrees. You will not damage the pipe with a power snake as long as you use the head that looks like a spring with a hook on the end. I have seen a spear head go through PVC. Unusual but it happened. Highly unlikely that settling cause a break in PVC pipe.