Did this happen following a repair, a hard (or not so hard) drop, liquid spill? Any incident?
In any case, there are 2 possibilities I can think about until you tell us more about the history of this device. If your device is out of warranty, here's what you can troubleshoot:
- Screen gone bad. Trying on a known good screen will confirm or rule out this possibility. Here's a guide that shows you how to try on another screen. It needn't be new, it can even be cracked, but it just needs to be known good. Alternatively test your screen on a different known good device.
- If a known good screen doesn't solve it, the touch circuit (and most probably a touch IC) has failed. In that case it stops being a DIY repair and should be taken or sent to a reputed repair store (it's a totally doable repair but at the same time easy to botch if the technician is not experienced enough) that can do micro soldering repairs or that subcontracts them to micro soldering experts.
If failed touch circuit does indeed turn out to be your issue, you can also have it replaced out-of-warranty at an Apple Store (provided it was never repaired by someone other than Apple before); but you'll loose your data in case you don't have a current iCloud or iTunes back-up. It's also your most expensive option, though guaranteed to get you back a working device.