You file a motion to compel, and ask the court to order them to do so. You also ask for attorney fees for the cost of bringing the motion.
If they still don't do so, you ask for sanctions (such as dismissing their complaint or a defense).
Yes, you file a motion to compel - but, attempt to work out the reasons why they haven't responded within the deadline to respond. Most judges do not want to be dragged into discovery disputes. If you can't work it out with the other party, then file a motion to compel.
You would not ask for attorney fees as part of that motion to compel. That's an entirely separate issue from discovery. Also, I highly doubt a judge would dismiss an entire claim over a discovery issue. Generally, if the judge is dragged into it, you or your attorney (hopefully you have one) would have a telephone hearing with the judge & other side over why they won't answer the interrogatories. Then the judge makes a ruling on that - sometimes the other side DOES have a legal argument for not answer some of the interrogatories.
So, attempt to work out the issue without court involvement, if that doesn't work, file a motion to compel discovery and the court will take it from there.