if it was a decent quality psu then a shut off at over powering is a good thing. its probably saved your system from damage...
all you can do is wait 10 mins with the power turned off at the wall. then try to reboot. make sure you remove the power from at least 2 fans and or a hdd if you have 1 spare in your system. it will either restart or just do nothing.... if it does nothing then its likely the psu has died as some dont reset 1s the over voltage protection is tripped.
5tdp just means thermal designed power. it doesnt mean it requires more or less votage...
the 88gt has a minimum recomended psu requirment of 450 watts. a maximum draw of upto 188watts.
the 560ti on the other hand has a max draw of less than 160watts.
the chances are your psu was on its way out anyway b4 you plugged the new card it. as a typical 400w psu will deliver about 320 watts constant and about 360 peak. if you take that and remove the 88gts power requirment then your left with less than 180w to run a cpu motherboard memory hdd,dvd and the fans. as you can see you were likely drawing peek power which would seriously shorten the life of your psu. when benchmarked the 88gt system drew between 209 and 280w but they were minimized builds with just enough to operate a cpu, cpu fan, hdd, mem,motherboard and 1 hdd.
the higher wattage numbers were on oc'd systems where the cpu and motherboard required more power for what was at the time an average 300-600mhz oc.
you need a minimum of 550w to be safe with a low/mid level ps today. so aim for that when you replace your current psu... also hope the psu did its job when it failed and protected your system.