Does the display flash 0:09 right away? It should show you SUN and 12:00am upon start up. If not, and your buttons are unresponsive, it may be time for a new timer. You can try replacing the plug and/or battery, but its probably going to save you alot of time to just replace the unit and save yourself a headache.
The plugs can be replaced if you can find them. The plug-in parts for the Vision series are different than most of Toro's timers, and are basically obsolete unless you can find them online. They have three bare wires and special specs, and it will be hard to find one specific to your timer. You can try the hardware store or Radioshack and see if they have one with three bare wires. You can find these specs in your owner's manual on the last page.
Internal transformer Models
Input Power: 120/230 Va.c., 50/60 Hz, 30VA
Output Power: 24 Va.c., 50/60 Hz, 22VA