Hi
RipGroove!
Was just passing through and caught your thread.
IMHO, the Samsung Galaxy S2 is still a very formidable phone and can hold its own with the majority of handsets out there, still. Now 3 years old but I still get given handsets to
root and update to
Android 4.4.2, KitKat, NEAT ROM which runs very light and fast and mirrors the Google Edition firmware on my S4.
The lack of response to your Wi-Fi problem is probably due to the fact that there is never, usually, one simple answer and so many variables involved. My first suggestion would be to go into Settings > Wi-Fi and delete your Wi-Fi connections, reboot and set each one up again. You could start with one, say at home, and see if that helps.
Secondly, you said that it happened after your update, to Android 4.1.2 I guess. You could download and re-flash your stock Samsung firmware by following the instructions and links in
#1.7 of the
Jelly Bean update - Dummies Guide.
Failing that, you could always root and flash the KitKat ROM mentioned. Its not hard, honest!