Proxies causing browsers to cease functioning

Question

My old workhorse of a G4 has been developing a memory problem of late--if the power cord is unplugged for too long, even in sleep mode it drains out, causing the clock to reset to 1969 and forget my current wi-fi password.  Now though it's developed a new problem--Firefox and Safari both claim proxy settings are getting in the way. I haven't changed any settings, and on a lark I tried clicking off the http and https proxies checked off and on, to no avail. 
Funny thing is, everything else works just fine--chat programs, email, anything online that isn't a browser.
So what's really causing them to be shut out?

Answer 1

As for the clock reset, it means that the tiny battery inside that keeps the time has gone dead, which is very likely to happen in any Mac over 5 or 6 years old. I was just reading another thread about that problem here:
https://discussions.apple.com/thread/3296298?tstart=0
If the large rechargeable battery is running out quickly, that just means it's old. Batteries of that era would start losing charge after 300 charge cycles or so, and after 4-5 years practically all laptop batteries (Mac or PC) will not hold much of a useful charge.
The proxy one is odd. I use proxy software, and I have to keep it up to date or some sites won't work. If you are sure the proxy check boxes are unchecked in your Network preferences, the next question is, have you ever installed any software that filters your Internet connection, like ad-blocking software, hacker protection software, parental control software, virus protection software, VPN software, anonymous web surfing software, etc. Some of those may act like a proxy server. If you have these, try turning them off to see if one is causing the problem, and if you find one that is, update it to the latest version.