Touch not responding properly when connected to laptop

I was wondering if anyone else is having/has had a problem I am getting. I plug my 5S into my laptop (as it needs charging) and I get the pop up on the phone asking trust/dont trust the computer (neither choice makes any difference). But as its plugged in (even before this message appears) the touchscreen becomes really unresponsive/laggy making the phone unusable. As soon as I disconnect from the laptop its fine again.

Any ideas?

Yes its connected with the cable supplied with the phone.

On you suggestion I tried a few different situations (disconnecting and reconnecting the phone each time) -

1) With case on, held in hand - response issues exist
2) With case on, lying on table - response issues exist
3) With case off, held in hand - response appears to be ok
4) With case off, lying on table - response appears to be ok

situations 1 and 2 are the scenarios that prompted this thread. But 3 and 4 I tried based on your suggestion. Clearly it appears having the case on somehow causes the problem, but how can this be?? Especially as in terms of the effect of holding the metal band around the edge in my hand, scenarios 1 and 4 should be similar as far as the phone is concerned.

I'm baffled!