I reviewed the thread, and I don't think it's the same error. I'll re-read the thread when I get home, and I'll check into it again. I'll bring this computer home and do a traceroute from both boxes to see what comes up.
traceroute is likely of no use here. The variable of interest is which IP your browser is choosing to use at the time of the request for the hostname involved. As noted in that thread, more useful would be to look up the IPs associated with www.perlmonks.org and repeat the tests directly against the IPs and report which of them have and don't have the problem.
I believe that the two major problems covered in that thread are already fixed (and fixed a long time ago).
Fairly rarely I notice that certain nodes cause a Perl (inside mod_perl) core dump when viewed by certain people via certain web servers at certain times. When that happens, my browser gets a blank page in response. Sometimes I can make this symptom go away by restarting apache on that server. Sometimes the core dumps persist even after a restart but, again, only for certain nodes and only when viewed by certain people.
Switching from perlmonks.org to perlmonks.com might cause different behavior because at the time, your browser is choosing to use different IPs for those different host names (and not all of the servers are in a state where that problem happens). Or the change may be because you have a login cookie for one hostname but not for the other. The useful information is whether you are logged in or not and what IP the request went to. The host name is pretty much of no use at all, since I have no way of knowing what IP your browser was choosing to use for that hostname at that time.
When I run into the blank page problem and I can't be bothered to try restarting Apache (which is more work than I think it really should be), I can usually see the information I'm after by using a hostname that I don't have a login cookie for or by looking at the parent node in order to see the reply or by looking directly at the reply instead of at the parent.
This happens so rarely to me that I have not spent the likely great deal of time required to narrow down the problem further.
Update: I installed ShowIP for Firefox as suggested by je44ery and ran through the same steps. (Thankfully, it's quite consistent.)
While browsing the site, the IP showed up as 126.96.36.199 for all pages, including the invisible/blank page. When I changed the extension from .org to .com in the address bar and reloaded the page, the IP remained as 188.8.131.52, and the page displayed just fine. As in the first time, the only difference is that when the page showed this time, I'm not logged in. I checked the cookies (via Tools|Page Info) and found that I have only the 'userpass' cookie on .org and no cookie for .com. Is there any information you'd like me to pull from my browser/OS/... to help? It's consistent, as I've tried the same sequence a dozen times over the last few days and always get the same result. (Note: on the work computer the "invisible" page comes up as a "network error" page as described in the OP.)
Well, I installed Wireshark, but don't really know how to sift through it efficiently, so any tips would be handy. (Or I could install another tool, if that would be better.)
In the morning, I'll restart my machine, flush out the firefox cache and capture a session. Then I'll save the session and start looking for clues.
Note: when I was able to read the content, it was by editing 'www.perlmonks.org' to 'www.perlmonks.com', which brought up the page, but I wasn't logged in. (Does that mean that an old cookie might be the problem? I used to use the .com address by default, but changed to .org when I started having some issues with .com in the time period of the previously-mentioned thread. The thing I find odd is when I bring up a new node and a minute later have the problem bringing up a different node. I would've suspected that the DNS entry would've been the same one.
If I find anything, I'll update the post and message you. If there's anything specific you'd like to see (other than what you just mentioned), let me know.