AJ,
I've owned an HTC One M7 in the past. There are 2 things that kept going bad on it.
a) the camera turns purple
b) the headphone jack breaks in stupid ways
Check your FM RADIO app or download the Next RADIO App.
If you launch it, and it doesn't ask you to plug in a headphone (to use as the antenna), then that is your problem. The headphone jack is engineered to fail, and it may think you have something plugged in so there is no sound on real speakers.
A workaround to your frustration (albeit a horrible one) would be to switch to bluetooth altogether.