As Reed pointed out you could access the Event Logs and see when they were created. AFAIK there are no specific event entries for system startup/shutdown, but you could look for services that are usually started/stopped with Windows. Though using this approach means it won't be 100% accurate, say if it crashes or it's manually started/stopped/restarted. One event I consider is the most accurate is EventLog service start/stop event.
if (EventLog.Exists("System"))
{
var log = new EventLog("System", Environment.MachineName, "EventLog");
var entries = new EventLogEntry[log.Entries.Count];
log.Entries.CopyTo(entries, 0);
var startupTimes = entries.Where(x => x.InstanceId == 2147489653).Select(x => x.TimeGenerated);
var shutdownTimes = entries.Where(x => x.InstanceId == 2147489654).Select(x => x.TimeGenerated);
}
Edit
Turns out there was a shutdown event. You can replace the Linq to get it:
var shutdownEvents = entries.Where(x => x.InstanceId == 2147484722);