It seems there is an IP conflict. Did you change default IP address of W8968?
Hard reset your W8968, login its web interface, change its IP to 192.168.1.3 and disable DHCP. It should work.

Note - I'm also pursuing this with TP-Link Support.

Yeah I changed the default IP to x.x.x.4, x.x.x.3 is taken by my printer.

Okay, so today I've been getting a correct IP address (192.168.1.21 in the DHCP range) but still no internet. The same problems continue if I choose a static IP (192.168.1.5) instead.

I've switched to the LAN2 port, the same problems so far.
In all cases I've been connecting via Wireless (except AP's <-> Modem/Router is ETH).

When I connect my laptop to the AP via ethernet, I get internet access, but the weird thing is I get the IP address 192.168.1.100, I've never seen one so high on my home network. But that's the default start for the TP-Link's DHCP pool. I've double checked, I have it set to disabled.

Something else I noticed, when connected to AP and I ping my Modem/Router it times out. But when I'm connect to the Modem/Router and I ping the TP link it connects fine.
(Maybe a firewall on AP? There's firewall controls on v1 and v2, but not on v3?)

Screenshots:
No Route Interface - https://www.dropbox.com/s/vc5nqif5rgkw002/Screenshot%202015-02-05%2011.52.44.png?dl=0
Pings - https://www.dropbox.com/s/hbu6zc7nror1asm/Screenshot%202015-02-05%2012.06.08.png?dl=0
Ethernet - https://www.dropbox.com/s/iivihmxmqmywyrs/Screenshot%202015-02-05%2012.46.54.png?dl=0

I've another update:
When connected wirelessly to TPLink-AP with no internet access, I can access it's web interface and reboot it. Then when I reconnect, it has both internet access and full local access.
However, if I connect to either my main router or my other AP, when I switch back to the TPLink-AP there will be no internet access.
So there's no internet or any LAN access outside of the TPLink-AP if I've been on another part of my network.

I rebooted the TPLink-AP, connected both my phone and laptop to it wirelessly. Both have full LAN and Internet, on my laptop I switched to main router and back to the TPLink-AP, phone continues to have full access, but my laptop is locked to the TPLink-AP. My phone sucessfully pings my main router, while my laptop fails to do so. My phone and laptop can ping each other and the TPLink-AP.

There does seem to be potentially some sort of an IP conflict between the TPLink-AP (x.x.x.4) and my main router (x.x.x.1). I say this because as long as the TPLink-AP is powered on, I cannot access the web interface of my main router, although it fixed when I restarted my main router.

Different APs and your main router are using different SSIDs?
Try to fix different channels for all of them.
What's the operating system of your laptop?
To figure out where the problem is, you may have to do more tests. Like you said, the phone works while the laptop doesn't. In this case, have you tried some other wireless clients?
If you restart the laptop instead of W8968, does it work as well?

All three are using different SSIDs (until I get the TP-Link working) and are all set (not auto) on different 20Hz channels (3, 7, 11).
Laptops is Windows 8.1 64-bit.
The phone (Android:CM11) works a little worse than the laptop; if I reset the TP-AP, connect to TP-AP with my phone, move to Belkin-AP or Cisco-Router, and return to TP-AP, my phone refuses it, where my laptop would connect with a limited connection.
My tablet is also the same (Android:Lollipop), and my girlfriends laptop (also W8.1 64bit) has the same problem as mine.
Restarting the laptop didn't change anything.

Here's a video describing my problem
https://www.youtube.com/watch?v=Nigs92HIMYQ

Here's a video of how I set it up, let me know if you spotted something wrong and I'll try address it. I pause the video a few times to help shorten it, the annotations say what I do/change (ignore the Youtube music)
https://www.youtube.com/watch?v=d22M_DoI7AQ