I had the exact problem (Windows 7 & NC 220.127.116.1189), I've checked Services in OS, and I saw that Juniper Network Connect Services is set to Automatic, but couldn't start.
Juniper Network Connect cannot start, if Public Documents (in Documents Library) is relocated. I have a habit of relocating Libraries (Win7 feature), to Data partition, not only because of old habits (not store important data on OS partition), but to fasten it's access (just one directory deep in root of data partition).
So this one folder must remain in C:\Users\Public, though I don't recall ever any file appearing in it. After changing back to default location, restart required. I'm considering to write this tip to Juniper, because even their page couldn't help me, nor their log files, when this had happened - I think they store this location hard coded, which should be corrected. No other programs I use produced this kind of error.
Hope this one helps.