Kenmore HT5 (something made by Whilpool.) Unit is 15 years old.

Unit turns on, allows you to select what cycle but when you press the start button you only hear a click. Drum nor heat start, reading online it sounds like the heater motor is shot.

Worth repairing it or would the costs be better put towards a new unit?

possibly door switch or control panel

Shot in the dark, since I don't remember the exact symptoms, but some of these Kenmore/Whirlpool's from this era had a problem with a relay frying.  Pull the top off the dryer, look at the control board mounted inside (not the front control panel, which is really just a bunch of switches).  If it's the relay, it should be pretty obvious... little white rectangular box that looks like it got way too hot, scorching the PC board around it.  I happened to have a "parts" washer of the same general type (don't buy these, btw ) I could scavenge the relay from, and got mine back up and running.  If that turns out to be what it is, shouldn't be too hard to find a replacement relay.

Make sure the rubber band didn't break. Easy fix

The click is the relay, check door switch, belt, if electric the high limit or thermal fuse. If the relay is bad you'll need the entire board so always check the cheap parts before you order a part for $150 bucks.