If you hover your mouse over the 'Online' icon it tells you the height/ date of the most recent block it knows about.
If you take your mouse away, wait a while and then do it again, has the block height increased ?
If so then it it syncing (perhaps slowly for some reason - peers vary).
If it isn't syncing at all then check your port 8333 is open and isn't being redirected anywhere (say to a Bitcoin Core on your network, something like that)
Thanks for your answer.
I'm using Multibit since.. 2013, I think.
I did reset the blockchain and after 3 hours it started to download blocks again, but extremely slowly (6-day package every 30 minutes or so, which isn't the speed I got used to).
I'll have to resync the blockain for 2-3 days, but it is good, as I will be able to send the funds to HD version.
Is there any way to get blocks faster?