I think for a full mpeg2 stream, you'd need in the ~16-19Mbps range, but if it's h264 or whatever the sling re-encodes to, you shouldn't need anywhere that high. I stream HD netflix all the time and have done so while downloading a linux iso. I think netflix says for their HD, you should have ~5Mbps. My gut says that it's the sling plugin. I find it odd that on two machines, it worked the first time (and both times there was someone else there, so I know i'm not crazy), and it hasn't worked since then. I've even tried uninstalling it, and deleting any reference to sling I could find, and reinstalling, and it still didn't work.
The two machines I've tested on, one was a Core2Due 2.2Ghz with Nvidia 8400M graphics (no hardware video acceleration), and an even older Turion x2 with radeon x1200 graphics (again, no hardware video decoding). I know that they can handle the feed, as they did the first time. I may try to scrounge up another hard drive, install a vanilla win7 and try again, and make use of the system restore to test if going back allows a second time in HD.