That's strange, that Chrome gives an error stating that IE needs to close. Are you sure about that part of your story? Or maybe Chrome gives another error message?
With me (and I don't have Chrome) both ntdll.dll and mshtml.dll are in the c:\windows\system32 folder. Aren't they with you? Can you check? If they really are missing, just reinstall IE8 from download.microsoft.com.
Here also, this are files typically related to IE, so it's unlikely they are used by Chrome.
These aren't TechRepublic files, but Microsoft-files, so TechRepublic certainly can't do the repair. Only you can. Or Microsoft can, if you pay them for it.
Two other questions:
1. Can you print any other page on any other site (only this specific article gives an error)? Or does any webpage you try to print gives this error?
2. If (but only if) it's this specific article that gives an error, can you give an exact link to it, so that somebody here can see what happens if he prints it. If all pages give this error, it's just an issue with your PC and trying here makes no sense.
When I try to print an article (via printer or print to a file using PDF software) off Tech Republic either by using IE8 or Chrome it will not print and provide two separate errors: 1.) that that page is being recovered, closes and then reopens under the same page & 2.) contains a dialog box the IE needs to close and send a reoprt in which an extension of a .DLL file is missing. Most topics that I've seen relate to missing the file (look in my recycle bin; which nothing is in there) or going into somesort of recovery. Is this something that a specific code can be used to repair this type of errors? Two errors today were that of missing items ntdll.dll and mshtml.dll. Would Tech Republic have any type or 'source code' to make a repair?