command or query to ping SQL server
I think you could run a query from SQL Server Management Studio from the machine that you can connect from and run the query with client statistics. That won't be exactly the same as a ping but you can see the server execution time (time from request sent from client to time server starts to send response back) and the client processing time (time from when the server starts to send to when the client receives it). That is why it isn't a ping because client execution time includes that network time and the time on the client to process.

I'd run a fairly simple query with a handful or so of rows returned. And maybe a slightly more complex query with more rows. You should also run each of these a few times in a row to eliminate any other slowdowns with the query.

Again, this won't really be a "ping" but it can at least show you some information and you can use this to trend information over time as well by running the same queries and looking at the info.

To look at client statistics - from within the query window of SSMS, go to Query and then select Include Client Statistics. You'll see the details in the Client Statistics tab of the results.

If you could also run SSMS queries on the actual server itself and run the same queries you can look at the difference in these times for the same queries and that should give a rough approximation of the impact of network latency perhaps.