First, what version of LANDesk are you running? I ask this becasue between 8.7 and 8.8 the location of the log files on the core server changed. In 8.7 the logs are located in ldlogon\provisioning. In 8.8, the logs are located in ldmain\log\provisioning. Additionally, the provisioning product is much more stable and reliable in the 8.8 branch of code. If you are not already on 8.8 SP 2 or SP3, I would highly recommend upgrading as many issues have been resolved with fixes in these versions.
Having said that, there are a few things to check in the process:
1. In which section are the actions added in the template?
2. How is the template being started, from the core or on the client side?
3. Does the target machine have a LANDesk agent installed?
4. Are you using distribute software actions or file execute actions?
5. If you right-click on the target machine in the task window, choose "View Provisioning Histroy". Are any of the actions executing?
This information will be helpful in figuring out what is going on.