If you don't know what the domain is, there is NO definitative answer...
e.g.
.co.uk exists, but is a different site to .com and different to .net
There are 13 gTLDs - generic Top Level Domains ( .com, .biz, .aero ) - in existence at the moment... plus loads of (200+) country TLDs ( .uk, .fr, .de, .us), many of which have second level domains ( .co, .org,) forming a combination ( .co.uk, .org.uk)
Given the HUGE number of combinations, plus the fact that the second level domains are generally administered by an organisation in the country which owns that country TLD, this gives an immense number of Registrars to check with.
So the solution?
Guesswork!
As to your problem on the LAN, I take it it's not resolving some / all of your URLs...
If I remember correctly, DNS is a hierarchical structure - if the domain ends in .com, your DNS server should point you in the direction of another DNS server resolving domain entries in .com, if it ends in .uk, it will go to the DNS which handles second level domains (.co, .org...) for the uk.
As for solutions, I think you will need access to the DNS server to update it's entries in some way.
Sorry I can't be more technical! Hope this points you in the right direction.
<marc>