Running a traceroute to your IPv6 address, (which you didn't quite obscure well enough in your image) it dies some distance away from you.
1 NOPE (NOPE) 0.570 ms 0.615 ms 0.715 ms
2 NOPE (NOPE) 28.731 ms 28.899 ms 29.085 ms
3 sixxs-asbnva-gw.customer.occaid.net (2001:4830:e6:7::2) 29.514 ms 33.038 ms 33.227 ms
4 sixxs-gw.hotnic.us.occaid.net (2001:4830:e6:7::1) 33.620 ms 33.331 ms 33.742 ms
5 10gigabitethernet2-2.core1.ash1.he.net (2001:504:0:2::6939:1) 45.001 ms 34.454 ms 45.105 ms
6 100gigabitethernet7-1.core1.nyc4.he.net (2001:470:0:299::2) 44.345 ms 37.767 ms 38.386 ms
7 nyc20.tbone.rr.com (2001:504:f::53) 40.832 ms 31.677 ms 42.384 ms
8 2001:1998::66:109:6:156 (2001:1998::66:109:6:156) 56.682 ms 61.804 ms 62.698 ms
9 2001:1998:0:8::35 (2001:1998:0:8::35) 62.859 ms 63.053 ms 2001:1998:0:8::ab (2001:1998:0:8::ab) 63.456 ms
10 2604:2000:0:4::2302 (2604:2000:0:4::2302) 58.353 ms 63.118 ms 58.478 ms
11 * * *
12 * * *
13 * * *
14 * * *
15 * * *
16 *^C
My best judgment tells me the last router to respond is at least two or three hops away from you, so I would say either TWC hasn't fully implemented it in your area and mistakenly turned on the DHCPv6 server too early, or they implemented it but are having issues. Either way, to get it resolved, you'll have to contact them. Good luck getting past first level support.
It might be 'internet security' software. I have seen broken IPv6 connectivity because of broken security software. Can you try from a different machine or a smartphone/tablet/etc? – Sander Steffann – 2013-09-03T07:27:43.300
First thing I would do would be to disable Hyper-V. If you suddenly get connectivity, then you have a configuration problem with Hyper-V.
– Michael Hampton – 2013-09-03T09:14:53.303@MichaelHampton Thanks for the tip. Afraid it didn't help though. I wasn't even able to use a webservice to ping the router's IPv6 address, so I think I'll just wait for the ISP to officially announce support. – Louis – 2013-09-04T01:20:55.087
Could also be a broken router. Beyond that, I don't think there's anything you can do except to yell at TWC for breaking the Internet. – Michael Hampton – 2013-09-04T01:23:44.123