I have been vexed by this error as well. For me it occurs in all web browsers. My son, also using a PC on our home network, also encountered it. Here are 3 actions we took that fixed the problem -- at least temporarily. I don't know all the details of why they worked. We are both running Windows 7 Home Premium.
1) Open a command prompt (Start -> All Programs -> Accessories -> Command Prompt), and in it run this comment (without the quotes): "ipconfig /flushdns". In my case I think a bad IP address had made it into my DNS cache, and once the right IP for paypal was determined via a real DNS lookup, all was well. However, another time I had the same error, this command did not fix it.
2) Control Panel -> Internet Options -> Content tab, click Clear SSL State. This worked for my son but not for me.
3) Clear the browser cache. I use Firefox, so this is done by clicking the Open Menu icon in the upper right, selecting Options, selecting the Privacy tab, then clicking Clear Your Recent History, selecting Everything as the time range, then unchecking all boxes except Cache, and clicking Clear Now. If you don't want to clear as much, select a smaller time interval first and try it. If that doesn't work, try a longer time interval, etc.
4) If you are using Norton Internet Security, disable Smart Firewall and then give it a try: In the task tray, right-click the Norton Internet Security icon, and select Disable Smart Firewall. Try accessing paypal. Whether this works or not, then re-enable Smart Firewall the same way. This worked for me; paypal.com remained accessible without the untrusted certificate error. We'll see how long this lasts. NOTE: I do NOT fully understand NIS's Smart Firewall, nor what it opened when I disabled it; do this at your own risk!
I have also seen others say that the date/time on their PC was wrong, and once they corrected it, the problem went away. There are other solutions offered as well by others, some of whom use different Antivirus programs and it is related to one or more of its settings.
If I find any more workarounds/fixes, or understand more about why the above fixed the problem (at least, temporarily) in my case, I'll edit or post again.
