Hallo, marley.
Now. I appreciate you've probably got Precise set-up just to your liking, and understandably don't want to disturb your set-up. That's fine; many of us are of similar mind.
Question; would you be averse to running a second, more 'modern' Puppy, primarily to obtain access to an up-to-date browser? I ask because Precise is getting very hard to find a functioning modern browser for; you have to bear in mind that most of the included dependencies are now well over 8 years old, and in tech terms that's like dinosaur status.
Yes, you can add newer dependencies, but they then want other, newer deps.....and further down the road, your glibc is then too old, AND your libstdc++, and a bucket of other core dependencies. You end up essentially re-building it into a more modern Pup, so why not just go with a new one to start with?
Is your machine capable of running a 64-bit version? If not, you might like to take a look at jrb's Precise-light; it's had a lot of stuff 'uprated' & brought more up-to-date:-
viewtopic.php?f=33&t=94
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If you can, though, a 64-bit Puppy just makes more sense, since everything is getting to be built as 64-bit ONLY nowadays. That's just the direction things are headed-in, I'm afraid.
Can you give us some idea of what your hardware specs are.....CPU, amount of RAM, storage, graphics (integrated OR a separate card, it doesn't matter), that kind of thing? It'll give us a better idea of what to recommend as your best course of action, but I suspect you'll be looking at a newer Puppy of some kind.
EDIT:- Hang about, I've just had a thought. What version of Pale Moon are you on? If it's still the 27-series, the updater for these no longer works. You'll need a modern, 28-series for that....
Mike. 
