It is possible a task may run longer than expected and you suspect something has gone wrong. It is even possible the task may cause a server to become unresponsive. Restarting the server will not stop the task, although it may make the server become responsive again.
To stop a Task, find the related task node (install: mysite.com) in the content list: /admin/content/node/overview, and delete it. This will stop Aegir from trying to run the task.
In the case of a site install, it may also be necessary to also delete the node for the site itself. The site may have actually installed properly. Verify the affected platform and see if Aegir imports the site. If so, you may need to reset the password to gain access to the new site. If the site doesn't import in the verify, delete any files from the sites folder on the selected platform and either try again and/or research why the task may have failed.
It can also be very helpful to try running tasks from the command line with drush (the entire Aegir web frontend is basically a user-friendly interface to a series of drush commands). You can see which command is being run by looking at a task node in Aegir. For example, if you are having problems verifying a site, you could run:
drush @mysite.com provision-verify --debug
Another option is to run the hosting task itself within the hostmaster context, which will then invoke the drush command on the applicable site. You can find the task node ID in the web frontend (look at the URL generated by Aegir to create the popup box which shows the log). If the task ID was 1234, you would then run this from the command line:
drush @hostmaster hosting-task 1234 --debug