I also am having problems syncing my cards from my computer to AnkiWeb.
When I have the app open, there is an arrow going in a circle next tot the Sync button and when I click Y or close out of the app, this screen comes up (see attachment). Eventually the sync times out and I have to start again.
I'm having the exact same problem, but for some reason the iPhone app has no issues syncing. Also any changes I make on my iPhone for some reason still carry over to my laptop anki even though the sync won't finish.
@Gabby, the fact that your iPhone is able to push changes to your computer makes me think that your computer isn't having problems with downloading changes but is having changes with uploads. My problem is identical. So... not really sure where to go from here but this is reassuring it isn't just my own device.