8800 Gigaset lights up but won't turn on.

I have seen that problem before, and it is a terminal one, sorry. You can put the batteries in backwards, and it will be okay. However, once it is set in the charger and the phone turns on, thats when the damaged occured. There is a power protection circuit (for surges), but I rarely see them open for this reverse polarity instance. The polarity reversal of the batteries does not kill the display itself (I know I have replaced them to no avail), it kills a circuit driving the display and I see the bad signals coming from the CPU which is a 80 zillion leg micro surface mount which is not cost effective to replace. Needless to say, I have about a dozen or so of them in that condition. You can google Siemens Cordless Telephone repair for repair or replacement solutions.