How to select gear on internally geared hub with broken shifter
From the image I'd guess your bike has Shimano Nexus 7 hub gear, though I'm not sure.

Anyway, the gear probably defaults to 1st gear when there's no tension in the shifter cable. So, riding your bike is very light probably because you are riding on the 1st gear.

What this means is that the hub gear might still be ok. It might've been stuck in the 6th gear earlier because either the cable or the shifter was stuck. Try attaching a cable back to the gear (it attaches to the bolt that is pointed by arrow in pic), pull it and see if the gear works.

If that's the case, you might be able to get a fully functional bike for a little money or effort - new shifters are not that expensive, especially if the gear is Nexus 7. It's a very common type and spare parts should be easy to find.