I had just made a Windows boot disk on a floppy for this computer, but in 'safe' mode, or any other, I cannot get around it freezing up. figured out how to do 'scandisk' from the DOS, and that didn't do anything. I ran a diagnostic thru DOS, and got a 'modem error.' Truth is, I don't know enough about DOS to get explorer OFF the machine, because I don't intend to use that computer for the internet anyhow, but as a learning tool for noninternet programs, to watch downloaded movies, when the kids are on the internet computer. Before it shut down, it was running one movie just fine, but it was slow due to the 85 percent fill....
If it says 'Explorer' and not 'Internet Explorer' then it basically means The thing that allows you to navigate folders. You'll notice that if there is ever an error with explorer the taskbar will disappear - as that is to do with navigation. So don't try to uninstall it - you'll end up having to reinstall the OS.
I'm not sure about the modem issue. It could be something to do with out of date drivers, corrupted drivers or an incorrectly configured modem. Check the settings and find the most up to date drivers for the device.
As a last resort, back up crucial data, reformat the HD and reinstall the OS.