For it to be the Blaster virus, this would have to be a system that hasn't been updated and patched for a long time (or a reinstall that hasn't been updated).

The virus usually causes systems to shut down randomly, not at the precise time of clicking on the 'Connect' button. Just in case, you can check for the virus:

Shutdown error. If your computer is infected, you may see this error message.

If your system is shutting down, follow these steps to stop the cycle. Then proceed to Step 2 to remove the worm.

To end the Blaster worm process

1.  Press CTRL+ALT+DELETE.

2. Click the Task Manager button.

3. Click the Processes tab.

4.  Click the Image Name column heading to sort the processes alphabetically by name.

5. Look for a process named Msblast.exe. If you find it, click the name to select the process, and then click the End Process button.

6. Close the Task Manager.

Other possibilities include faulty modem or drivers, or maybe an overheating problem. It would be good to check that the system is clean, fans working etc. You could also check out the modem by swapping it for another, or creating another dialup connection to call an ordinary phone or mobile. Then connect using the connection you've created.

System restore to a point before the problem began is worth trying.

Scanning for a virus is worth trying too.