I repaired one of these the other day and initially replaced the digitiser which didn't solve the problem..turned out to be the slider flex. If I'd followed my hunch that it was the problem I could have saved myself a whole lot of tooing and froing taking it apart and resitting connectors. Take a good look at the slider flex, it's the most vulnerable part..if it looks worn or kinked from all the sliding then I'd replace it first. I don't recall it being part of the step by step guides and had to work it out for myself.. follow the guide for the display removal and then you'll see how the flex feeds through the bottom portion etc. It has 2 simple flip connectors and uses adhesive tape to keep it in place.this is the part I ordered in the UK, I'm sure you can get them in other countries.
As only half your screen is unresponsive it does sound like the digitiser (touchscreen) is the problem like this
for the slider flex Sony Ericsson Xperia Play Digitizer Replacement and at step 11 flip over the silver backing of the top slider portion and you'll see the flex and it's attachment coverings..I managed to work it out.