Think having the BellSouth Tech check things concerning your connection issues is the best way to go. It does sound as if your modem is having trouble in some way.

System Restore reset is the next thing for you to do.
  1. Log on to Windows XP as an Administrator
  2. Right click the My Computer icon on the Desktop and click on Properties.
  3. Click on the System Restore tab.
  4. Put a check mark next to 'Turn off System Restore on All Drives'.
  5. Click the 'OK' button.
  6. You will be prompted to restart the computer. Click Yes.
To Re-Enable System Restore, follow steps one to six and on step four remove the check mark next to 'Turn off System Restore on All Drives'. A new restore point will automatically be created.

Take a look at this link PROTECT YOURSELF FROM MALWARE: Tools & Tips
from PhillePhan on keeping the computer clean.

The things I use to keep the computer clean and well maintained of course are a good anti-virus program and firewall.
I also manually update and use, weekly, AdAwareSE, Spybot Search & Destroy (including the Immunize portion of S & D)

The key program I use, I feel anyway, is SpywareBlaster
and keep it updated and enabled weekly for both IE and Firefox (which I use for everything except Windows updates). What is really great about this program is that it does NOT run in the background so it won't use valuable resources. Also use the Restricted Zone portion of the program.

Instead of allowing my email to "flow" directly into my Outlook Express I use a neat little program called MailwasherFree. Using this I can filter out any mail that is junk, or from those I do not know. I keep this program minimized all the time and my Outlook Express Closed until I check the new mail with Mailwasher, if I know the sender I allow it to come on into Outlook Express, if I don't I delete it from the server using Mailwasher.
DON'T store old mail, as you have found, some of those you had did contain viruses. If it is something you NEED to keep, print it out and then delete it from the computer.

I set my browser cache on both IE and Firefox to no more than 10mb and history to keep at 7 days.

I do all my updates, except my anti-virus program, manually. For Windows I always accept the critical and or security updates, others I pick and choose.

I run the built in Disk Cleanup weekly and then use the ATF-Cleaner every 10 days or so.
I also recommend using a super defrag program called Auslogic Disk Defrag
I learned about this super free program from Turcoloco here on this forum. Works much faster than the built in defrag program and does a super job.

That is pretty much what I recommend. These steps have worked well for me.
Let us know what you find out from the BellSouth Tech. Plus maybe it could help others too having the same issues.
Happy I could help, please don't be a stranger either. We like it when all of our members stay in touch.
Judy