That changes things a bit. If it had not livened up at all I would be thinking electrical issues.
Anyway such a thing typically gets called a boot loop.
I tapped in sony xperia play boot loop and a variety of things came up to fix it (some mentioned something called ftf) so it seems like it is a known issue for some models. Do be aware that some types of restoration like this will wipe the phone, some will not -- some just want a working phone where others will want data recovery and be willing to put in some more effort. Check to see beforehand what a given set of steps will do. Most likely the user data will be on a separate partition and this is more concerned with the boot partition but do check anyway.
If you search for your model number and boot loop it will hopefully yield a solution for that one. At that point it should be standard means to grab whatever you like from it (I like FTP rather than messing with USB or SD cards to play it how you will).