moen single handle tub/shower

Hello, Hoping someone can lend some advice. We just bought an older house - built in 1975. There is a single handle push/pull Moen tub/shower combo in the master bath. The sink (which is close to the plumbing for the shower, runs beautifully). When the knob is turned to the hot water side...

I haven't ever used this shower ( I know, I know) since I have other showers in the house. Went thru inspection today to sell the house and the inspector found that aside from not getting any hot water to one tub/shower unit, when the handle is turned 'past' the hot water making, the cold...