the answer you got from the store is bogus.
If you had an IP conflict, you wouldn't be able to do anything...no internet...nothing. because your modem and router would be fighting each other.
You say it had been running fine for the first day or so..... What changed after that ? Did you change any settings in the router setups ? You might try a hardware reset on the router....using a pen, push the little tiny button on the back of the router for 10 to 30 seconds..... You WILL lose any changes you have made to the router setups, so if you changed anything, go in an write them down before using the reset button.
I run my router from my battery backup unit (and also my modem) to make sure the electricity powering the router is stable as possible. Personally, I think electrical problems affect many people without them being aware of power problems because they may not impact your tv or microwave, but routers seems sensitive to them (my opinion only).