You should consider installing Slingplayer 1.5 instead of using Web Slingplayer. At least until Sling Media fixes the problem with their servers. Slingplayer 1.5 isn't dependant on the Sling Accounts which could be causing your problem to connect. You can also use a direct IP address Slingbox Directory entry to also bypass any problems has with their Slingbox Locator Service.
If your ISP is providing your router with a DHCP address, then you'll need to sign up with a Dynamic DNS service for your router to duplicate the propietary Slingbox Locator Service for the Slingbox. Nice thing about DDNS is that you can sign up for them free and its an internet accepted standard. Opposed to the Slingbox Locator Service which is propietary to the Sling Media ecosystem.