Firstly, do you have SP1 for Dragon Naturally Speaking? It can be downloaded here.
Secondly, I agree with the suggestion of upgrading to IE8.
Next, I would next check for any add-ons in Internet Explorer that might be being misbehaving. If any look Dragon-related or Nuance-related (the manufacturer's name) then disable them and resart IE. If you can browse and scroll without problem, you'll have determined that it is not IE at fault, but the Dragon Naturally Speaking software itself.
In this case, the next step I would suggest would be to try a repair installation of the Dragon Naturally Speaking - unless everything works as you want without the add-on of course.
Go into the Control Panel, into Programs, look for the Dragon Naturally Speaking and click the Change or Repair button. If you get another option to Repair, click it and let it run through the wizard. Then restart.
Check in IE and re-enable the add-on, if required.
Failing this, I would contact Nuance support, advising them of the troubleshooting steps that you have just tried.
To do this, simply press F12 to bring up the Developer view, click the Cache menu, and select Always refresh from server. The next time you load a page in that tab, it will redownload everything every time you navigate.
This setting will not carry over to other tabs or be retained when you close the browser, however.
Best Answer
For me the same symptoms were caused by leaving Developer Tools console open when closing Internet Explorer (after fixing the problem I tried and succeeded in recreating the problem, by leaving it open again).
The fix for this situation: