I can't speak to the heat-bed, i have never tried to go above 80. but a couple things to check on the hot-end.
1) make sure that your thermistor (the glass ball on the end of two little wires) is firmly pushed into your hotend.
2) make sure that the fan on the heat break is off when it is pre-heating. I had a similar problem, where my fan was cooling my hotend faster than it could heat.
3) try a new heater cartridge/resistor, (the can shaped thing in your hotend). I'm on my second, you just sometimes get a defective one, or one will go bad, i would advise buying a 3 pack off ebay.
4) Don't trust your printer's layout, if you have a way to independently verify the temperature of the hot-end, like with an IR thermometer or a multimeter and thermal-couple. If the temperatures between what your instruments see and what the printer see are more than 25% different, then that means that you may need a new thermistor, or your firmware is set to a different type of thermistor (like a 150k instead of a 100k)