SQL Server instance using only a few hundred MB. Well below the minimum server memory setting
The memory counters in Task Manager or Resource Monitor are not a good way to determine SQL Server's memory usage. If SQL Server is using locked pages, these do not show in the working set or private bytes.
There are many ways to determine if SQL Server is using locked pages. You can look for a message like the following in the error log:
Using locked pages in the memory manager
Or, check the sys.dm_os_process_memory DMV locked_page_allocations_kb column. For example, on a local test instance using locked pages I see this:

Whereas Resource Monitor shows:

Note this is different from the sys.dm_os_sys_memory DMV you mention in the question comments.
There is all sorts of other useful memory usage information in the DMVs, including high-or-low virtual or physical memory indications. These are all described in Books Online.
It seems probable that someone has granted the SeLockMemoryPrivilege to the SQL Server start-up account recently, or the account has been changed to LocalSystem, which has this privilege by default.
Generally speaking, locking pages in memory is a good thing.