There was a well known issue a while back - a batch of Sony CCDs were found to be faulty and suffer from sensor failure. Good news - it's a known problem with your model an it's free fix, even out of warranty!
Bad news, it doesn't sound quite like your problem - the affected CCDs often displayed purple/green streaks...
Have a read here:
http://www.imaging-resource.com/NEWS/1130908577.html
Hope this is the case - if not you're probably looking at throwing the camera away. You could scout ebay for a 2nd hand A2 (an A1 with a better EVF), go for another bridge camera (Sony R1, again 2nd hand, is maybe the most tempting - it's got a cracking lens and a CCD almost the size of those found in DSLRs) or go with an entry level DSLR (the closest to your A1 is the Sony 300/350 - both of these have proper liveview with proper autofocus and imagestabilisation - pair one up with something like a Sony/Tamron 18-250 or maybe a Sigma 18-125. Otherwise go for a Canon 400/450 or Nikon D40/60 with a stabilised lens - gonna cost though).
Good luck!