Here's how you solve this sort of problem in XP...
Step 1 Do a google search for the .exe or .dll you are concerned about. Look at the answers given by more than one source. Bleepingcomputer.com is good, as is processlibrary.com.
In this case, adeck.exe looks like it might be an audio driver and it also looks like it is non-essential - it can be disabled without doing any harm.
Step 2 Disable the .exe so that it doesn't load at startup. Start>Run>(enter the following) msconfig>OK and look for the process under the tabs marked 'Services' and 'Startup'. Uncheck the box next to the service. Click OK and Restart.
Step 3 When your computer restarts, check the box which says 'Don't show this message...'. This will make sure you don't keep getting a reminder about it. Done!
Alternative Step 3 Download and run CCleaner. Click 'Tools', then 'Startup'. Look for adeck.exe and uncheck it. Restart the computer. Done!
Any problems, just retrace your steps and recheck the boxes. Use these tools with caution. If you uncheck things without taking care, you might create more problems than you solve.
I would also suggest you download, update and run Malwarebytes AntiMalware to check for anything that may have disabled your Taskmanager, then look here:
http://windowsxp.mvps.org/Taskmanager_error.htm