Shimano 7 speed with click shift not enough range. Can only get 4 of 7 gears The indexing shifter (lever for down, click for up type) doesn't seem to have enough range to cover the entire 7 gears. Limiting screws are all the way out. If I adjust the cable I can get 4 lower gears or 4 higher gears or anywhere in between, but only 4 gears.

The shifter display will only go down to 4th. It's like there just isn't enough range in the shifter to cover all 7. The dérailleur can move the full range.

The bike was bought almost new with very minimal use and as far as I know the gear set is original.
The problem is for sure in your shifter. Make sure both levers can move freely at any gear (i.e. are not hitting against brake lever mount or other accessories).

Also make sure that your shifter's inner mechanism looks fine, parts move freely. If not - consider lubrication.

Disconnect cable from the derailleur, take shifter off the handlebar, shift to the lowest gear and try shift 7 times up. If you can't so the only option is to replace it to proper 7 gear shifter.