This is a handheld vacuum cleaner with a simple circuit inside. I’ve charged it fully for a good while and also tried decharge-recharging it but no joy. All it can manage to do is ticking the engine which is not powerful enough to get it on full rounds and working. I have contacted the producer and they said they don’t have batteries available for this item. Is there a way I could find out if it’s the battery or something else? I find it a waste to put this in the bin and buy a new one. 
P. S. I have a video but it doesn’t seem like I can upload videos here.
Update:
Here’s how I’m testing it with the 9V battery:
Update #2:
I’m not sure if the contact is made but here’s how I’m testing and still no joy. I have a feeling that I’m making a mistake somewhere.
Best Answer
Easy fix if it's the batteries
The batteries are 18650s they are extremely common they are used in power tools, laptops, home devices and they are even the driving force behind the Tesla automobiles.
Test
Cut the red and black wires going to the batteries one at a time. Strip off a little bit of insulation and apply them to a 9 volt battery. Red+ black -
Leave the yellow wire for now. It senses the voltage for the charge indicator light. It's possibly connected to a chip wrapped in the battery casing.
This is what the individual batteries look like
CAUTION
These batteries have a lot of kick. They are potentially very dangerous if the contacts are shorted. They will melt wire and are very capable of starting a fire.
If the unit runs on a 9v then the batteries need replacing. If that's the case you will need to order some Amazon has lots of them. You'll want to find some with the same mAh rating. In your case you will need two 1300mAh batteries.
something like this, basically apply power directly to the motor.