Here is the official HP quickspecs document for that PC - unfortunately it still shows the E6700 as the best it can run. As these pre-built PCs are very locked down and require propietary BIOS updates to support different CPUs then anything newer or better just won't work. Looking online, it sounds like the Q6000 series CPUs don't work on that system for the same reason.
The E6700 chip is very good for overclocking, most get over 3.5GHz. Unfortunately, HP motherboards don't support overclocking so that wouldn't be an option.
If you are looking to upgrade the motherboard then you are best off buying a new case - perhaps something cheap and good like
this one. I say this because according to
this parts and service map, the DC7700 uses a non-standard motherboard layout - so any off-the-shelf parts (ATX standard) will not fit in that case.
If you do want to change the case then you will also need a new power supply, as the HP one is non-standard size and only 240W.