If the potatoes are just old and are not actually bad or rotten then you will not likely get sick or ill from eating old potatoes.
However if the old potatoes are actually rotten and squishy and you eat those rotten old potatoes then you could get sick.
Eating rotten potatoes can lead to solanine poisoning.
When you get solanine poisoning you can experience symptoms of solanine poisoning which are headaches, vomiting, fever, stomach cramps, and difficulty in breathing, diarrhea, hallucinations and shock.
If you do experience any of those symptoms of solanine poisoning you should go to urgent care or the emergency room for treatment.
If you have old rotten potatoes you should throw them out and not risk getting sick or dying from them.