I would try different pools as well.
Specifically one where you know they have implemented vardiff - variable difficulty
I can say that
www.kano.is has this as probably most pools do. All pools who primarily mine bitcoin probably have either their main or a specific port with vardiff.
I call pools major and minor for one reason. They either primarily mine bitcoin and have one or more significant attributes or they have many coins and do not have a significant bitcoin mining hashrate.
https://bitminter.com is a long-standing pool who has been around for years.
http://mining.bitcoin.cz is Slush's pool and has a large hashrate.
I would try these three pools before any other to check my functionality.
I do not see this to start some flame argument with other forum members, as I know some are vocal if one leaves a specific name off a list, but these have been used in my experience. YMMV
Can you post a screen shot of a couple of screens? Make sure you block out any details which could be used against you. Most cover their user name, even if it is address, many still cover it. I'm not paranoid either
The miner status screen would be a great start.
I'll assume you bought it from e-bay, a forum, etc, but not from someone you know? Did they share a screenshot of it hashing? Can you share such? If not, what if any details did they provide?
Firewall? I don't see how anything "standard" would do it.
When you say you tried every configuration suggested what does this mean exactly? What items have you changed / tried?
Worst case maybe a reset or firmware something or other. I have upgraded and downgraded many different brands of miners, but I, most unfortunately, was not aware of Bitcoin when the S1 was in its prime and do not own an S1.
The good news is there are many, many people here who have.
I am not recommending you load firmware. I only recommend such if you are doing it for a known reason, not as a step to try when throwing shit at the wall to see what sticks.
In my opinion, the absolutely best thing you can do is read miner threads. I spent weeks reading entire threads here that were old, older, oldest, some that span all of the above. I read the 'official" threads from Bitmain, Spondoolies, and then started reading the others. Over-clocking threads, now under-clocking threads, and in general any hardware thread. I started taking notes and have a good troubleshooting sense. The miner threads have over and over corrected for me what you said is your biggest weakness. By the way, that is all of us. We all get stuck on the tiniest, crappiest, most fubared detail, and eventually get it to click, --- or find out we'd have to spend too much money to do so, heh
I wish you the best luck in getting it going.