You need to get scandisk to work to have any chance with Disk Defragmenter. When scandisk seems to stall it often means it has encountered a bad cluster ( bad sector  ) on the hard disk. This it will try to repair and the process can take quite a time to complete. If this is what is happening then the only way forward is to be extremely patient. You may find it prudent to back up your more important data.

I suggest that you remove Temporary Internet Files ( including Offline Content ) and History. Start Settings, Control Panel, Internet Options, General, Temporary Internet Files, Delete Files, check Offline Content and click on OK. Also empty  your Recycle Bin. This helps remove a potential problem when running Scandisk and Disk Defragmenter.

Another precaution. Delete the contents of the applog folder ( the content not the folder! ). See link below (disregard the references to the error messages ) for the procedure.

Defrag Error Message: ID No:DEFRAG00205 (Q238165)
http://support.microsoft.com/default.aspx?scid=kb;en-us;Q238165

I would then run a "thorough" Scandisk again in Safe Mode. For Options see that System & Data areas is selected. Then click on Advanced and see that you have selected:

1. Display Summary -Always.
2. Log file -Append to Log
3. Check files for -Check all three options.
4. Report Ms-Dos Mode name length errors

There is an option to Automatically fix errors which I would check but many computer buffs do not preferring to investigate the error using the log before attempting to fix the problem.

When you have successfully run Scandisk run Disk Defragmenter in Safe Mode.

To start Windows in safe mode Click Start, and then click Shut down. Click Restart, click OK, and then press and hold the CTRL key until the Microsoft Windows 98 Start-up Menu appears. For some machines, you can use F8 instead of CTRL to bring up the Microsoft Windows 98 Start-up Menu. Enter the number for Safe mode, and then press ENTER.

Notes In safe mode, Windows uses default settings (VGA monitor, no network, Microsoft mouse driver, and the minimum device drivers required to start Windows). You will not have access to CD-ROM drives, printers, or other devices.

Disk Defragmenter Hangs After Choosing Disk to Defragment
http://support.microsoft.com/default.aspx?scid=kb;en-us;218160

Please let the group know how you get on whether you succeed or not. If it fails please give some information about your hard disk, it's size and whether it has been partitioned.