The screen does not respond to touch.

There can be multiple issues on your iPhone. Check the battery of your device; if it is not performing up to the mark, the screen goes blank all of a sudden or it is a classic case of unresponsive touchscreen.

To check battery health: Settings > Battery > Battery Health.

You can put your battery on low power mode. The option is available right there.

Apart from battery health, you can check that the screen guard is in perfect shape.

Take other corrective measures like:

Force restart

Restore Your Device As New

Restore Your iPhone Using Recovery or DFU Mode

Get Rid of the Unwanted Data

Update iOS on Your iPhone

If nothing works, you can contact Apple Support

If you replaced the screen yourself, then that would explain the issue, but the only way to deal with a disabled device is to restore it via Recovery Mode. See this, If you forgot the passcode for your iPhone, iPad, or iPod touch, or your device is disabled - Apple Support

Our iPhone 8S suffered a shattered screen about 10 mos ago, and was disabled by our service provider to allow us to replace it with a new iPhone 10.

I replaced the screen in the broken i8S about 1 week ago, but can not complete restart, even with phone support by our supplier, leaving it with 2 messages displayed (iPhone is Disabled connect to iTunes & Emergency), and with no consistent touch-screen operation, nor ability to nonsectarian to iTunes through our MacBook Pro.

is there a site with diagnostic instructions and explanations such as what is (DFU mode) for this phone, since it's off warrantee and all the Apple stores are closed due to COVID19 ?

Sorry- Siried again: can't connect to iTunes not "nonsectarian"