Hello from Irvinebank!

I have purchased an new iMac with Snow Leopard (OS 10.6.1).

What do I have to do to make my Limewire 4.18.8 Pro work?

When I search I get no hits.

is it connected? How many green or blue bars do you see at bottom left of screen or are they all red?

I have only one green bar

That's why .. only one green bar means you are not connected to the gnutella network. We'll need these details: System details - help us to help you (click on blue link)

I can still use Limewire Pro with my old computer, Powerbook G4 15''. But on my new iMac, I get the brick wall wich says Limewire detects a firewall, but when I check my system requirements, it says the computer's firewall is turned off.
Hardware:
Model Name: iMac
Model Identifier: iMac9,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2.66 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache: 6 MB
Memory: 2 GB
Bus Speed: 1.07 GHz
Boot ROM Version: IM91.008D.B08
SMC Version (system): 1.44f0
Serial Number (system): YM9261350TF
Hardware UUID: E9C282FD-1C6A-5A46-8EF7-D0DB299B4CE7

I can't find where it mentions how many bits I am using.

Bit's no concern for LW 4. I suspect your issue is needing a 'fresh' gnutella.net file. Find a link to it near bottom of If LW 4 Will Not Connect (click on the blue link). An alternative one here http://www.gnutellaforums.com/343558-post10.html

Also, make sure your LW is not using same port as your other computer. ie: LW prefs -> Advanced -> Firewall.

Hey!

I downloaded the new free version and it worked. Thanks for the help. Can I download the new Limewire Pro without having to purchase it again, and will it work the same?

Depends when you purchased it. Pro usually only has either 6 or 12 month support with updates. If that time has passed then the answer would be no.