DSC-T33 completely blank in the screen. But, showing date & time display along with menu

First thing I would do is reset the camera. This is a fairly easy procedure which involves either going into your setup menu and choosing "reset," holding down the menu key for 5 seconds, or, removing the batteries for a few minutes. It may be that the firmware loading got corrupted and the camera just needs to be "rebooted," which is something that turning it on/off won't accomplish. But after which, you should have the camera reset to factory default settings.

Another tip is to go to Sony's website and look for firmware updates. Download and install them. If none of that works, then it mostly likely sounds like a faulty CCD chip. Sony ran into problems with some models getting faulty chips last year. Check the SONY website for a product advisory. The good news is that if this is the problem, SONY should replace/repair it for free.