When my computer starts a message appears saying C:WindowsSystem32 fnyxll.dll cannot be found. How important is this file, and how can I stop this message from appearing?

It seems this is quite a rare message, as I was unable to find many references to this file during my research. However, some of the references I found related this file to adware and spyware. As a starting point you should download and run Ad-Aware SE Personal (www.lavasoft.de), Spybot Search & Destroy (www.safer-networking.org), and Windows Defender (www.microsoft.com/downloads) to check for any threats which may have found their way onto the computer. While this is unlikely to resolve the error message, it should remove any underlying causes so we can fix the error and hopefully it should not return.

Once the scans have completed we can try manually removing the reference to the file which is causing the file to load on startup. Go to the ‘Start’ menu > ‘Run’ and type ‘regedit’ (without the quotes) and click OK. In the Registry Editor window, navigate to the following registry key:
HKEY_LOCAL_MACHINESOFTWAREMicrosoftWindowsCurrentVersionRun
In the right-hand pane, look for an entry relating to the ‘tfnyxll.dll’ file. For example, you may find an entry with something like ‘C:WINDOWSsystem32
undll32.exe C:WINDOWSsystem32 fnyxll.dll’. Once you have found such an entry, right-click on the entry and select ‘Delete’. Next, navigate to the following registry key:
HKEY_LOCAL_MACHINESOFTWAREMicrosoftWindowsCurrentVersionRun
Repeat the same procedure. However, don’t be alarmed if you cannot find any entries relating to ‘tfnyxll.dll’ in this key. I don’t expect that you will, but it is worthwhile to check just in case.

After removing the entries from the registry, close the Registry Editor. Now we must check whether the ‘tfnyxll.dll’ file has actually been removed from the system. As the error message indicates the file cannot be found, it should no longer be present on the system. However, since the file may be related to adware or spyware, we should double-check. Open My Computer or Windows Explorer. You must first enable the viewing of hidden files and folders to see the Windows system directory, which may contain the file. Go to the ‘Tools’ menu > ‘Folder Options’. In the window that appears, click the ‘View’ tab. Enable ‘Show hidden files and folders’ and untick ‘Hide file extensions for known file types’ then click OK. Now, navigate to the following directory:
C:WindowsSystem32
Sort the files by name, and look for the file ‘tfnyxll.dll’. If this file is not found, it looks like the file has gone. However, if you do find the file then rename the file to something else, such as ‘tfnyxll.old’. As I could not identify the real purpose of the file, renaming it will allow us to restore the file if necessary. I suggest you monitor the computer over the next few days and, assuming nothing goes horribly wrong as a result of renaming the file, you should be able to safely delete the file.

After you have finished the above procedures, restart the computer and the error message should no longer appear on startup.