The Connect Box (assume that’s what you have?) should have no green lights on, and only the white bar. That’s the state when everything is working.
When booting up (which takes a few minutes) or when something’s wrong you’ll see more lights. From your description it looks like your wifi is good and your internet isn’t (flashing green means it’s trying to connect).
If you’ve been playing around with the settings it’s worth resetting the box (there’s a button or something on the back I’m sure).
Check the cabling both ends, then ring UPC and ask them to check that your internet connection is ok. They seem to have really improved their call centre recently. Each time I’ve called they’ve answered almost immediately and have a system in place to find an English speaking advisor if you need one.