What's wrong with my iSi soda siphon, and how do I fix it?
I'm fairly sure that you should be able to get a "rebuild kit" with all the rubber parts (and perhaps a few others.) Due to the wonders of modern commerce, it's anybody's guess as to whether you might well be able to find a complete new siphon for less cost. If you have a second-hand store or frequent tag sales you can almost certainly find one barely used for less cost - lots of people get them and don't actually use them.

It certainly appears that the main gas seal at the charging port is toast, at least. 

The instructions on mine included complete tear down diagrams as far as I recall - many things unthread to expose innards (such as the big slot on the white plastic part.) I have not actively used it in a few years, but I don't recall the process being all that difficult (but it was a bit off-putting to find the accumulated bits of metal seals that had blown into the mechanism over time.)