Hello Sonikdreem, thanks a lot for contacting us through the Intel Communities.
There is a list of all compatible processors with the Q965 chipset, but I suggest you to check with Gateway in order to find out if the processor can be changed. Sometimes upgrading is not an option that depends on the system.
Remember that if you make changes on OEM systems, the product is not going to be covered under warranty anymore.
You can check if the Intel® Core™2 Duo Processor E6400 can be installing on the system.
This is the list of compatible processors with one of our Intel Motherboards DQ965WC