Recently we worked on an issue where none of the saved list or site template can be used to create new list or sites respectively. We do see the templates in galleries but when click on create we dont see them as an option. We noticed that in list template gallery none of the templates were showing featureId and version infromation as shown.
and for site templates we dont get an option to activate the solution
To get this working we need to set the parserenabled value for the web to be true, which is True by default but in rare cases we have seen this value getting toggled to False.
$web = get-spweb <url of the web>
$web.parserenabled = $true