After the most recent round of updates to my XenServer 7.0 installation (up to XS70E036, but not sure whether that has anything to do with my problem, as I also upgraded my XenCenter to 7.1.1 per update notifications), I am no longer able to see the console in XenCenter–it just remains white/blank.
I've tried connecting from different installs of XenCenter on various machines, and, based on what I read in reported issues, also made sure my connection isn't NAT'ed (it's on the same local network as my one and only XenServer node), but still saw the same issue.
I tried the latest XenCenter 7.2.0 on multiple machines: no luck. Then 7.1.1: same thing; then 7.0.1: still a blank console. At this point I was really suspecting the hotfixes I applied (after which I rebooted the server, so I was sure the new toolstack was running), but there's no easy way to uninstall the applied updates, so I was stuck. I seem to recall just a couple months ago, before applying XS70E033, XS70E035, and XS70E036, I was able to see the console, perhaps using version 7.0.1.
Eventually, I found the original XenCenter 7.0.0, and, surprisingly, it worked! I double-checked the newer version on another machine and it was still bad, but as soon as I downgraded that install, it worked, too!