Just to clarify things, TTL is irrelevant to the speed.
You will get the same TTL even if you ping from the internet :
http://www.his.com/cgi-bin/ping?
The Latency is obviously high(That is what is affecting the speed) and as you can see, the time it is taking to get a return packet jumps from 45milliseconds to 439milliseconds as soon you leave the DM network(212.36.211.33) so it must be a problem on their side..
It is funny you say you feel like you are on dialup because the previous IP address is registered as residential dial up - That does it mean it is dialup though :-)
http://tools.whois.net/whoisbyip/
inetnum: 212.36.199.0 - 212.36.223.255
netname: IDM-RESIDENTIAL-DIALUP
Hope that helps.
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