When very few systems show in the Ansys toolbox, this means workbench can’t access the license features for these analysis systems. If it is a license served from another machine, you can’t always restart the license server, and this may not be the solution anyway. You may just have a disconnection on your network to the license machine. You should be able to run the “Ansys Client License Settings” in the program menu, and then press “Features in Use.”
Older versions may require a different selection to get this information, such as “FlexNet Publisher License Status” or “Gather Diagnostics.” See if it can access the license server, if the daemon is up, and finally the features listed. There are several features that allow opening Mechanical for static structural or modal, buckling: ansys, preppost, mech_1, mech_2, etc…
It may also be that the license is up and the features exist, but if your company has few tasks of each feature, they may be all taken by other users. The number of licenses issued and in use will be reported for each feature.
You might need to specify the license port and host under the first selection: “License servers.”