Even though we don't know what changed, it is obvious that something has.
I suspect it will be nearly impossible to 'remember' what that was since it started "a few weeks" ago. It may be the dreaded voltage spike or even a too long period of low voltage. You may not have even been home when that occurred. A good, reliable, but not cheap uninterruptible power supply (UPS) will prevent these events.
A second "common ground" possibility is that you have a not-to-well protected WiFi setup. I assume you are living in an apartment complex or at least fairly close to neighbors? What type of password are you using (I think WPA/WPA2 Personal is about all you can do in System Prefs->Network)?
One question: What are the ages of the two computers?
Emptying the browser's cache, at least in Safari, is super simple. Use the "Empty Caches" item in the Develop Menu. If you don't have a "Develop" menu, go to Safari prefs, Advanced and check the "Show Develop menu...". Once you have done that, you can then disable the cache completely. Develop Menu->Web Inspector, click on the "Network" column, click the item near the extreme right-hand end of the row just below the column labels. It should change color from
black to
red lines:
[attachment=3550:disable_caches.jpg]
Private house, but neighbors not that far away! Yes to WPA/WPA2. One computer 2010, the other 2011. I will follow your advice. Thanks.