Some possible causes and solutions for no display on the A600 are:
1. The batteries may not be installed properly in the handset. Take the batteries out of the handset and put them back in, making sure the flat side of the battery is against the spring. Put the handset back on the base and see if "Charging" appears on the screen. If it does, then give the phone and hour or so to charge up and see if it works.
2. Make sure the phone was not accidentally powered ‘OFF’ by pressing and holding the End button. Simply placing the handset back in the base will immediately power the handset back ON if it was powered OFF.
3. If the screen lights up but there is no display and the Torch light is on, the phone is not working right and needs to come in. If the Torch light is off, try adjusting the contrast setting.