I can't open the dmg.

I'm new here and have read loads of threads, and have included a few suggestions in other threads.

My limewire dmg downloads, but when I double click on it I can't open it.
I have plenty of space.

When I couldn't open the dmg, I deleted it, emptied the trash did disk utility repair, restarted computer.

Went to the OSX Firewall instructions posted by Lord of the Rings, downloaded the Java 5.0 but I couldn't load it as the hard disk had a red exclamation mark. Rechecked and I had already an updated version.
I then downloaded limewire once again - this time when I double clicked on the dmg I got the message "not recognised" !
Have no idea where to go from here.
Hope someone out there has an idea for me.
Thanks in advance
Matilda

These are some more answers to the questions, but I don't think they are relevant.

Mac OSX 10.4.8
Only firewall ticked is Gnutella/Limewire
768 MB DDR SDRAM
18.11 GB available HD space
Broadband
Linksys ADSL Gateway AG041- UPnP is enabled. Administration port is 8080
This model isn't listed in the link Grandpa listed.
Connecting from home
Trying to open latest version of Limewire - doesn't get recognised
Java 1.4.2 plugin setting
Java 1.3.1 plugin setting
Java15 release 1. dmg - can't install
Internode is my service provider
it says "your test worked"
Not sharing with other computers
New problem, an experienced user using other versions of limewire now deleted
yes I saw the blue brick wall
I don't have any anti-spyware, or ant- virus programs