So basically you don't have anyway to start your PC from the front panel of your new case? So you're expecting to just turn on the PSU switch and get the PC up and running?
No HDD activity lights? No Reset Button? No Power Button?
Yes you need that. The only way you'll be able to get that PC started will be by bridging the soft power pins on the Dell mobo... Which are somewhere in that Connecter on the motherboard. Good luck finding them.
This isn't going to work dude.
You need to buy a new motherboard and an OEM operating system.
Take all the components off the Dell Mobo and rebuild. Oh yeah, you'll also need a new HS&FAN, because the one that comes with the Dell, is special for the Dell CPU Mounting Bracket.
Trust me on this... I owned a Dell 8300 and have worked on hundreds. They are proprietry and can't be upgraded easily.
Sure, videocards, memory, soundcards or PCI cards... But that's it...
May-be even CPU's... But cases, PSU's, Motherboards... No can do.