There are 2 basic things (other than an incorrect set-up) which can prevent PINGS. 1 ) the device may not respond to PINGS. 2) a firewall might not let PINGS through. I wasn’t quite sure with your set-up whether your first successful PING reply was on the same PC in which case it might have been a ‘loopback’ reply you received, in other words it didn’t actually go anywhere outside your PC.
If you are using Windows you could try using TRACERT ip address (from the Command Prompt), this should give you a step by step reply and enable you to see where it is getting stuck. DDNS suppliers and ISPs have also been known to block PING requests. See below a successful example of PING to a public DNS server
C:\Documents and Settings\Peter.MyPC>tracert 158.43.192.1
Tracing route to cache0003.ns.eu.uu.net [158.43.192.1]
over a maximum of 30 hops:
1 2 ms 1 ms 1 ms 10.10.30.4
2 58 ms 61 ms 58 ms dr13.ennby.ov.easynet.net [89.200.128.198]
3 60 ms 57 ms 57 ms 5acf001e.bb.sky.com [90.207.238.30]
4 59 ms 59 ms 59 ms be2.er10.txlon.ov.easynet.net [195.66.226.43]
5 60 ms 61 ms 59 ms ge5-0.BR1.LND8.ALTER.NET [195.66.226.16]
6 61 ms 61 ms 59 ms so-2-3-0.CR2.LND8.ALTER.NET [158.43.254.37]
7 62 ms 73 ms 62 ms ge-1-0-0.XR2.LND9.ALTER.NET [158.43.252.46]
8 61 ms 61 ms 61 ms POS2-0.GW9.LND10.ALTER.NET [158.43.150.129]
9 60 ms 59 ms 59 ms ge-0-0-0.lnd10eusoesr2.lnd.ops.eu.uu.net [158.43.150.114]
10 62 ms 61 ms 62 ms cache0003.ns.eu.uu.net [158.43.192.1]
Trace complete.
Regards
Peter