I have downloaded latest version of Limewire on my Mac w/Snow Leopard latest version and it just won't open.

There might be a flaw with your original Java installation. Try setting up a test account & see if LW will open from there.

Also, get Information for the actual Program; Command i. You will see option to Open in 32-bit. This can be changed, but if you are booted into 64-bit then I'm guessing this should be unchecked. Mine is checked & I"m using intel macpro with snow leopard.