IPad doesn’t rotate anymore

There's currently no way to do this system-wide. If you make the app you're using for the demo, you should consider making the app do the rotation for you.

Design the app so when it's in landscape mode it displays a portrait mode screen (ie, the app always appears rotated on its side). Then hold the ipad in landscape mode, turn rotation lock on so it stays that way, start your app, then use your app with the correct orientation. Turn your monitor on its side to see the faked portrait mode.

You can also do this for presentations if you turn all your slides on the side.

However there's currently no way to do this for apps not designed for it.

Take it to the Apple store. They will not only help you be sure it's hardware but explain how they would get you an equivalent device for a known cost with Apple's warranty on the "repaired" iPad part. They might even be able to speculate if the case shows damage that might make a determination if it's more/less likely that you have a wiring or glass/digitizer issue.

Then you can decide if you want to buy a used iPad and try to scavenge parts or buy a new digitizer and roll the dice to guess if it's the screen or the connector or the chipset on the main board that turns the raw signals into a touch event.

Once you know your "official cost to replace" you can decide if you want a DIY project or perhaps pay someone that repairs iPads professionally to offer a repair that might be cheaper than Apple's but have less of a warranty than getting something factory made or factory refurbished.