QdotJ
Time to call in someone else to assist you. Any further tinkering could cause further damage. 

 
It'd probably be cheaper to buy a replacement adaptor, assuming you mean take it to a repair shop.  I don't think it's an issue with the socket on the card itself.  Although honestly, I feel like EVGA should send me a replacement adaptor, since it was included with the card.
 
Update: 
Sent in request for new adaptor, unfortunately its going to take at least a week.  Hopefully the new one fits correctly

The importance of a good quality PSU cannot be overstated.  Since you now have a new card, and a new monitor, I suggest getting a new PSU.  This would solve your issues.   Fortunately.  PSU's even decent ones aren't that expensive.  I would suggest one of the new EVGA models, or even Corsair.  If you want to spend a little more go with SeaSonic.
 
A 500-550 watt would do fine, but I always suggest going for a little more- like these 600 watt units.
http://www.evga.com/Produ...aspx?pn=100-W1-0600-K1
 
http://www.evga.com/Produ...aspx?pn=100-B1-0600-KR
 
Here is an even better unit:
http://www.evga.com/Produ...aspx?pn=210-GQ-0650-V1

New adaptor finally came in, same problem. I've pushed as hard as I can, but neither cable will go into the 8-pin socket on the card. 
 
 
 
 
Edit:  Tried again with the first cable...finally got it to go in. Hopefully the card didn't get damaged in the process.....