Hello, I recently purchased a new GTX 1060 FTW+ on Amazon.  Card is brand new in original package, tightly sealed.
When I opened the box I noticed that it has no driver install disc with it, or any connector for my monitor to hook into. My monitor is very old, like 10 years, but I have always been able to connect to my older cards, a 450 and a 560TI. The older card came with a exterior connector, but they seem slightly different and won't fit on the back of the new 1060. Old connector had 4 small pins around flat connector, new card has the flat slot, but not the other 4 pins, so it wont plug in.
 
Do these cards not come with driver discs or connectors, ( I saw a unboxing video and that guys card had a driver disc at least) or are they simply missing from my package?
 
Thanks.

This is the only Cable that Comes with your Card:

 
 Did you get your EVGA Case Badge?
                                                   EVGA Case Badge

DO NOT BYPASS THIS "but not the other 4 pins, so it wont plug in."
Do Not Make Shift a Analog To Digital Connector. Use on a DVI-I Port Only.
You only have a DVI-D Port and you CANNOT USE the Analog To Digital Connector on your Card.
DVI-D, DisplayPort, DisplayPort, DisplayPort, HDMI  Time for a New Monitor.
 

 
A DVI-D connector on a graphics card sends out a digital signal only, while a DVI-I connector, which carries both an analog and digital signal, can send out a digital signal (for digital displays such as flat panel LCD monitors) as well as analog signal (for older displays such as a CRT monitor) using a DVI to VGA adaptor shown below.  The graphics card shown in Figure 1 which shows a DVI-I connector contains more pins than the DVI-D connector shown in Figure 2.  The extra pins on a DVI-I connector carry the analog signal which the DVI-D connector does not have. 

Using the included adapter with two 6 pin PCIE power plugs to the single 8 pin PCIE power plug will work fine. Plug two 6 pin plugs in, not just the one.
 
It's the Molex to PCIE power adapters that have been known to mess things up badly on occasion.

Well, now I'm not sure what to do.  First I had a issue plugging the 6-pins into the adaptor, I think one of the pins was bent. I managed to straight it enough to get the second 6 pin in, but now I can't get the 8-pin end to plug into the card. I pushed as hard as I dare, but it still wont go in. The metal sockets don't seem perfectly straight, but it doesn't really feel like they are the part resisting. I've tried evening them out with a paper clip, but it doesn't work

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