If I were you I'd move away from TalkTalk, I know a few people who've got their phone and/or broadband service and none of them like it.
To be fair, I don't know any UK broadband provider that actually "supports" Linux either, to the best of my knowledge they're all M$ / Mac focussed.
That said, I've been running Linux successfully for quite a few years now, initially with NTL (now Virgin Media) and for the last 12 months with Sky. I've never had any problems connecting to the Internet from a Linux PC with either.
You might need to take a look at your configuration though. I don't know anything about Solaris, but I assume your network card is configured to acquire its IP configuration via DHCP and that the DHCP server is enabled on your router. If that's the case, and it's not working, you could try setting up a static IP configuration instead, see if that works.
My router and PC are currently configured as follows:
Internal IP address = 192.168.10.1, subnet mask 255.255.255.0
External IP address, subnet mask, gateway, DNS server etc. acquired from Sky Broadband
IP address = 192.168.10.10
Subnet mask = 255.255.255.0
Default gateway = 192.168.10.1 (i.e. the router)
DNS server = 192.168.10.1 (the router again)
This works like a charm - maybe something similar might work for you?