To simply check that the service is running following IF statement is sufficient to do so:
if (service["Started"].Equals(true))
{
lbl_eid_deliver.Text = "SERVICE: Running";
}
else
{
lbl_eid_deliver.Text = "SERVICE: Offline";
}
However, there is a another method that can be used to do same thing by using ServiceController.
An example can be seen in the link provided below.
http://stackoverflow.com/questions/178147/how-can-i-verify-if-a-windows-service-is-running