The good news is that Slingplayer, the TV streaming app, is coming to the iPhone soon. The bad news is that your old Slingbox doesn't work with it. Here's Sling's reasoning.
As the product team was working on the future roadmap we realised that the hardware on the older boxes would not support the kind of high quality streaming video and advanced features across all platforms we want to offer moving forward.
This is why it doesn't work with the Slingbox, Slingbox AV and the Slingbox Tuner, and only with the SOLO, the Pro or the Pro-HD. This seemed weird to us, since 640x480 of the original Slingbox was fine enough to watch on laptops even outside the local network, why wasn't it enough to watch on iPhones with even lesser resolution?
Their answer: the decision was based on the entire roadmap, not just the iPhone. So, they've got some more interesting things coming up that they decided that NOW was the time to make the cutoff on old devices. It's true, the old devices are lacking in processing power, and no matter when they do the cutoff people will be upset. Might as well be now.