Well. First of all I don´t think it will support a Core 2 even if its LGA is 775, because, it has a P4 installed, right?. I tried it before just to find that it was impossible (that´s not me writing there, but I used the explanation here http://www.tomshardware.co.uk/forum/208814-28-pentium-core).
If you want to upgrade it seriously, apart of the very clever addition of 4 GB of RAM, you should think in passing all the components to a bigger case, but, WARNING!!, I have done it and discover that the frontal USB and audio is kind of propietary, and the ones that comes with the new cases did not work, so you must have to do some frankenmodding to make it fit your new case.
Also this step will make possible the build of a proper system of fans to cool properly the components, HP computers usually run very hot because their technicians apparently do not take in consideration what airflow and overheat means for a computer.
The HP PSUs, even if they are VERY noisy, are quite good, made to work 7:24 365 days, they have very good components,active PFCs, etc. but the one that´s mounted on the dX´s is the MINI version of them, so you will have to replace it. Invest some more money to get a decent 450 watt PSU.
The MOBO of HP´s pcs are quite extrange, I have tried to mount a disipator like the one you say, but the screws did not match the holes on the MOBO, and the capacitors are placed so the alluminium heatsink crashes with them making almost impossible to use one of those. I have finally used a Zalman CNPS5X Performa, modifying the bracket a bit to avoid hitting the capacitors. Depending of the orientation you use (I use a upward position to make the air blows to the top of the case directly to the upper exaust fans) you should modify the integrated GPU´s heatsink cutting some of its fins, because the cpu heatsink hit some of them.
For the GPU, maybe I will go for another model. The UEFI problem is there, I´m afraid. I have successfully mounted a Nvidia GT220 OC 1Gb (modified with a 90 mm AuraII fan that dropped temps in several degrees) and recently a Nvidia GT740 OC 2 GB DDR5. Both options are great if you don´t plan to play very modern games!, this cards, because the P4 it´s abit old and not very powerful, make the system can only run 2009´s games at 1280x1024 at MAXIMUM (with very good fps), but most recent games must run in lower settings, they can´t run at 60 fps at MAX settings, but, fortunatelly and overall with the 740, tey´ll do never under 40 fps.
Well. I hope I helped. I did some mods to a dc7100, and this computers are hard as a rock, good buy for 10 bucks!!