first, I moved your post into the right community. It is better placed in "LANDesk Management Suite - Software Distribution" than in "Servicedesk - General".
Now to your question, have you checked the LANDesk Scheduler service on your coreserver? Is it up and running?
Yes, I checked this first and even restarted it, One machine failed all others at still pending. Any suggestion
If you are running 9.0 SP2 with Some MCPs see if there is a process called TaskQueue.exe running on the client.
Sorry I don't see a process called Taskque.exe on the client or the console, we are running version 2011-0428, is this the latest version?
Do your clients have the 0428 patches installed or just your core?
How about, just deleting the old stucked Task and retry it with a new one?
If this works and will never happen again, you can invest your time in something better.