Unable to open Secure Websites

Hello-
First off, this question applies to Internet Explorer, Opera, and Netscape web browsers.
I have had the same Windows XP PC for about 7 years, and have had my Inspiron laptop for 2. However, they both have started to have trouble displaying Secure websites in the past two days. This is generic for all three web browsers that I previously mentioned. The sites in general that I've had trouble with are the log-ins on PayPal.com, eBay.com, and webkinz.com (my sister's). It will eventually show the page and allow me to log-in, but takes about 6 minutes to load, as opposed to the usual 2 seconds. And then when I try to log-in, it usually takes too long (20 minutes +) that I just have to give up. However, rarely (usually in the morning right when the computer has been turned on) the sites will work fine.
I've been browsing the internet for the past two hours looking for ways to fix this issue. I've entered in all the commands under the Run button, I've deleted the complete browser cache and cookies, and I don't suspect this to be a firewall issue since my laptop has McAfee and my PC has Norton.
Any ideas what might be up with the system? Could it be an issue with the router (which I've had for two years, and it has worked fine...)?
I might add that sites like Hotmail and Key Bank still work fine.
Please let me know if you can help...
Simon