it would be very possible if you have spyware or some type of virus that is connecting through your pc to their home base on the internet. That is exactly what happens when a computer has been taken over and is part of a bot net you lose control of the pc. They have programs that are put on your pc that "phone home" and take their orders to do what ever it is they want to use your pc for.
Could be something else but usually when you hear things like there is a connection on my pc that I am not creating then that is often the issue.

What antivirus and antispyware programs are you running on your pc and are they updated?

I would suggest going to an online virus scanner and letting it scan your pc from there because anything on your pc may have been disabled by them if that is the case.
Get a FREE Online Virus Scan that is a good one, you must use IE for it.

I would also get these 2 free programs if you do not have them, install, update and run the scans.
SUPERAntiSpyware Free Edition
Malwarebytes' Anti-Malware
Please download Malwarebytes' Anti-Malware to your desktop.

* Double-click mbam-setup.exe and follow the prompts to install the program.
* At the end, be sure a checkmark is placed next to Update Malwarebytes' Anti-Malware and Launch Malwarebytes' Anti-Malware, then click Finish.
* If an update is found, it will download and install the latest version.
* Once the program has loaded, select Perform full scan, then click Scan.
* When the scan is complete, click OK, then Show Results to view the results.
* Be sure that everything is checked, and click Remove Selected.
* When completed, a log will open in Notepad. Please save it to a convenient location. The log can also be found here: C:\Documents and Settings\Username\Application Data\Malwarebytes\Malwarebytes' Anti-Malware\Logs\log-date.txt

Are you using a firewall on this pc? if not you should go immediately and turn on the built in Windows firewall that will give a little protection but you really should get a firewall if you do not have one.
Start> control panel> security center> turn on firewall

Let us know the results of those scans.

Thanks ravencajun! I do have a firewall under Norton 360 and should be protected against browser hijacks, viruses and spyware. In fact, my files were updated and scans automatically run on Friday night and no problems were found. BUT, i am on my way to do the online scan right now.I'll let you know how it goes.
Thanks a bunch!
Ida

well once we make sure it is not some nefarious programs on the pc causing this then we can move on to seeing what else it might be, one step at a time.

You can go to your event viewer and look there to see if you are seeing any other accounts listed as logging on also.
start> control panel> administrative tools> event viewer there you will see options for system, applications and security, the security area is the area you can view all log on and log off info, you can double click on each item to view more info, I would go through all 3 areas, look for red and yellow flags and log in info.

Well, I am back. I have spent the whole afternoon and half the night downloading and scanning. Nothing showed up, so then I did a deep scan with my Norton program. Nothing came up except for one low risk tracking cookie that was removed. Then I did as you suggested and went to the event viewer. Under security, a lot of logons came up besides mine. Like: Local Service, Network Service, System, NT Authority with "Anonymous" being the logon attempt. Some say Success Audit, some say failed audit. All of this may be perfectly normal, but I'm just reporting back so maybe you can tell me where to go next. TIA!Ida

May want to call your Internet Service Provider and see if they know anything, the only other thing I could think of is to try a repair connection, go into control panel look for network connections see the link for further instruction.

Here is a link that might be useful: Repair connection

Thanks zep. I will call tomorrow but I don't think it is an ISP problem. My son has a particion (msp) on my computer and the Internet disconnects just fine from his side. Also, my backup computer disconnects without any problem. Both show how much power is going in and how much is going out, but on my side, nothing. 0 coming in and 0 going out. Just as if my computer is being bypassed!Ida

Your probably right not an an isp then, Maybe Norton is causing some problem but I'm guessing now could try to disable it and see.

OK I went back into the View Log under Applications, I found several of these messages: Remote Access (with the dates and times) The user XXXXXXX, (my acct,) successfully established a connection to ITC, (my internet servuce) using the device Com3.
Don't know what to make of it.
Ida

do you have remote access enabled on your pc? do you use remote access? Are you using windows xp PRO?
This link should be helpful to look at and see if you have remote desktop enabled on your pc and how to disable it also. There are multiple pages.
Remote Desktop

I have never allowed Remote Access on my computer. That's like sleeping with your door open... but I checked Properties on My Computer and to my dismay, I found the block for Remote Assistance was checked. It never has been before! I am running XP Home, so Remote Desktop was not an option. I unchecked the Remote Assistance box. I have a feeling this will take care of the problem of Remote Access, but it's still a mystery how it happened. Now to check all my accounts for fraudulant charges. Thank you again!! Ida

you are very welcome, I always check that on any pc to make sure it is not enabled with out my knowledge, if you get a nasty on your pc sometimes they have the ability to change those options and next thing you know you have company! and not in a good way!

I have become paranoid since you guys turned me on to Event Viewer. I check it several times a day. My disconnect problems seem to have gone away, but something is still not right. When I log on to the Internet and then check the log viewer, under Security, I get 2 identical entries with my name on them. But the event # is different. One is is 528 and one is 538 straight down the list. Both are successful logons, but the 528 shows the logon process as Advapi. Not Advapi.exe, just plain Advapi. Google says it could be a virus or trojan. I have already spent a whole day scanning and came up clean. Does anyone have any idea what is going on? Should I scan again? If I should get rid of this Advapi, how would I go about that, as it is not on Add/Remove. I really would appreciate any help!! Ida

Windows XP records event 528 for user logon and 538 for user logoff.

Advapi not sure what this is but I do not think it is a trojan with out the exe in the file.

Others will add more