mghig :
After a bunch of Googling, I see that the XPS 8300 should be able to run the 650Ti Boost or HD7790. I'm also interested in the Sapphire 7870, would anybody know if this could fit in my case and be compatible with my motherboard (0Y2MRG)?
http://www.amazon.com/Sapphire-DL-DVI-I-SL-DVI-D-PCI-Express-100354OC-2L/dp/B00A2J4ROE/ref=sr_sp-atf_title_1_1?s=electronics&ie=UTF8&qid=1388086292&sr=1-1&keywords=radeon+7870
So far your Sapphire card requires 500 watt PSU and two 6-pin ancillary power connectors, however so far I was able to find XPS PSUs with only one 6 pin connector and 4 SATA power connectors (2 SATA power connectors can be converted into one 6 pin connector), so if you have only 1 HDD and 1 DVDRW you can attach your Sapphire to DEll PSU, if you have 2 HDD or 2 DVDRW - you can not. Also, 500 watt falls short of 460 watt actual.
I can guarantee to some degree that Dell PSU is really 460 watt, but I would not push my luck with 500 watt GPU. So, PSU upgrade for this card is required.
Regarding actual fit. Any card at about 10.83" (inches) long will fit, even a bit longer should fit, but one SATA cable would have to be changed for longer one. So your card is 8.46" - perfect fit.
So, final answer - you need PSU upgrade to accommodate your Sapphire Radeon HD 7870.
Generally any ATX power supply should fit, it could be tight fit however. Make sure that new PSU has at least 4 SATA connectors and two 6 pin video card ancillary power supply connectors.
Anything else I can help you with?