Thanks, lagomorphmom! Yes, I indeed use Firefox, and the only time I don't have service is when the power is out, so I guess I really haven't needed to reboot the modem. And this is the only computer I have, so I'm pretty sure there is no router here.
For some reason, this computer just doesn't like IE any more. I've been using Firefox for a couple of years, but last week when my sis was visiting, she tried to open her e-mails using IE, not knowing that I don't use it, and it gave her all kinds of fits. I told her to start over and try it with Firefox, and it worked just fine. Any reason why IE just won't work here?