I would like to know more about 'TTL' when pinging. Why would an answer "request time out" and tell me that the link is down? I thought the answer would be "destination host unreachable" instead?
TTL is the "Time To Live." Of course, that explanation doesn't help much, because packets aren't alive, and TTL has nothing to do with time. TTL is the number of routers a packet can pass through before it is dropped. Each router that forwards a packet decrements the TLL by one. So, if a packet starts out with a TTL of 128, it can pass through 127 routers before it gets dropped. You shouldn't ever worry about TTL, though, because it only becomes a factor when a packet goes around-and-around in circles in a 'routing loop.' You can get just about anywhere on the Internet in less than 30 hops, so the default TTL of 128 is fine.
You'll get a "request time out" message when a router simply doesn't respond to a Ping or Tracer message (collectively called ICMP messages). This might mean that the router is offline, or that the router has been configured to ignore ICMP messages. On the contrary, you'll get a "destination host unreachable" message when a router does respond to your message, but it doesn't have a route to the destination network. This usually happens in one of two circumstances:
1) The router has been misconfigured.
2) The destination network you specified doesn't exist, for example, if it's a privately numbered network such as 192.168.5.5.