I will use my machine as an example.
I do not know your level of knowlege with Solaris, so I am going to assume your a noob...I am having you use echo to avoid messing with VI, pay attention to the >> and >.
echo "192.168.1.100 deeznuts" >> /etc/hosts
echo "deeznuts" > /etc/hostname.hme0
echo "192.168.1.1" > /etc/defaultrouter (this will be the IP of your router connected to your DSL)
echo "search verizon.net" > /etc/resolv.conf
echo "nameserver xxx.xxx.xxx.xxx (ip of your router) >> /etc/resolv.conf
cp /etc/nsswitch.dns /etc/nsswitch.conf
Now either reboot (the easy way) or do it manually...
ifconfig hme0 plumb
ifconfig hme0 deeznuts netmask + broadcast + up
route add default `cat /etc/defaultrouter`
You should be able to get out to the internet now, if not there might be something I might have missed or something else you have to look into.