Check if a server is available

Just use the System.Net.NetworkInformation.Ping class. If your server does not respond to ping (for some reason you decided to block ICMP Echo request) you'll have to invent your own service for this. Personally, I'm all for not blocking ICMP Echo requests, and I think this is the way to go. The ping command has been used for ages to check reachability of hosts.

using System.Net.NetworkInformation;
var ping = new Ping();
var reply = ping.Send("google.com", 60 * 1000); // 1 minute time out (in ms)
// or...
reply = ping.Send(new IPAddress(new byte[]{127,0,0,1}), 3000);

If the connection is as unreliable as you say, I would not use a seperate check, but make saving the data local part of the exception handling. I mean if the connection fails and throws an exception, you switch strategies and save the data locally.

If you check first and the connection drops afterwards (when you actually save data), then you still would still run into an exception you need to handle. So the initial check was unnecessary. The check would only be useful if you can assume that after a succesfull check the connection is up and stays up.

From your question it appears the purpose of connecting to the server is to use its database. Your priority must be to check whether you can successfully connect to the database. It doesn't matter if you can PING the server or get an HTTP response (as suggested in other answers), your process will fail unless you successfully establish a connection to the database. You mention that checking a database connection takes too long, why don't you just change the Connection Timeout setting in your application's connection string to a more impatient value such as 5 seconds (Connection Timeout=5)?