Think you are getting correct help so far.

All I got is Centos 6 doesn't work Centos 7 works. You said disable iptables and 6 works.

Assuming you have configured request correctly. https://www.gnu.org/software/wget/ma...9-Options.html

If you can't fix your iptables then consider either an online tester or program like FWbuilder to fix what you have. As far as I can tell from thread you have a firewall issue.

I guess while tables are off you could monitor the traffic to prove ports used maybe? Port 563 may be required for ssl? Dunno for sure.
This should have worked.
iptables -A INPUT -p tcp -m tcp --dport 80 -j ACCEPT
iptables -A INPUT -p tcp -m tcp --dport 443 -j ACCEPT

May have to flush on changes. iptables -F

That wouldn't have helped. OP is trying to go OUT not have something come IN. Possibly adding those rules to OUTPUT chain instead would work:
iptables -A OUTPUT -p tcp -m tcp --dport 80 -j ACCEPT
iptables -A OUTPUT -p tcp -m tcp --dport 443 -j ACCEPT

But the OP has a rather involved setup where he is first doing "DROP" rather than "ACCEPT" on the OUTPUT chain itself, His rules for 80,443 within the OUTPUT chain is jumping to a completely different (and customized) chain. Adding the 2 rules above to OUTPUT itself would possibly obviate what his jump rule is doing. Since I don't know why the setup there is cutomized as it is I'm loathe to suggest adding a rule anywhere than to the jump chain specified by the existing OUTPUT chain rule.

P.S. I'm not sure why you mentioned CentOS7. The OP says he is using CentOS6.2. If it WERE 7 instead he should use firewalld to configure rules as that is a front end for iptables on RHEL7/CentOS7. Directly editing iptables on 7 would likely cause issues because it is expected that only firewalld update iptables there. This isn't true of 6.2.

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I only suggested trying the most simple rules to test. As you see their rules are not working correctly. A validator may help.

The OP said this. "Unfortunately the other server (CentOS 7)"

Hi Guys,

Yeah, I think only mentioned the CentOS 7 machine in the context of demonstrating that the sites I was trying to access were working properly, and the fact that (at the time) I didn't think I could compare iptables set-up with that of firewalld.

Anyway, after much debate (inside my head), and still not really understanding why it is that the chain wasn't working, even though it seems set up okay, I decided to try the following (which, I'm sure, is still not the best way, but I just need something to work):
Note, prior to this I already had made a back up of iptables in case I needed to revert, but it did actually work, and I can now make the requests I need. I believe, in order to retain this change on reboot, that I need to save the changes, which I did with:
Thank you very much for the assistance, most especially mensawater: your patience and knowledge were much appreciated!

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