Have an AVERATEC D1002UHC-1 ALL IN ONE with processor core 2duo E4600, speed 2.6 GHz, memory 2Gb. Can I replace the Intel core 2Duo by core i3 and increase memory to 4 Gb?, my actual memory is 2Gb PC-2 5300 DDR2
The i3 is not compatible with your socket but, provided you have enough ram slots, you can upgrade your ram. Just make sure you get the right type.
Edit: Just realized you said it was an all in one. Even more important that you note if your ram is normal or if it is sodimm memory (ie notebook size). You may find is time consuming to take apart your all in one to upgrade if it doesn't have an easy access ram compartment.
The answer is no.
The Core2 Duo uses a LGA775 socket.
Core i3 uses a FCLGA1156 socket. Doesn't exist on the motherboard in your system. Your BIOS wouldn't support this CPU architecture, either.
The Core2 Quad is also a LGA775 socket processor. You would need to contact the manufacturer of your system to determine if it is even possible to use a 65 Watt Core2 Quad Processor like the Q9550S on your motherboard. It may require a BIOS update.