yes, i agree on your point on Linux, Let's go through the usual suspects

Assumptions are that your connecting to the Interent at home using a DSL (Broadband\ADSL in the UK) router connected to the ethernet\nic\network port (not usb)
- if your using a USB modem - pass....you'll need the drivers for the modem from the manufacturer

Check the the lights on the router & your able to tets it's functioing using another computer

First Test - Start a Web Browser - usually Firefox. Whatever the page, try another page,e.g. UNI - Ente nazionale italiano di unificazione - Versione Italiana or Sun Microsystems

Second Test - Open up (or start a Terminal session - search around for the Terminal Option on the solaris menu
Type the following (excluidng the # symbol)

# su -
(enter you password when prompted)
# ping www.unix.com
(you should recieve 4 lines of replies, if not, post the result)

We'll get onto chking the Network Interface Card if you still stuck