Please check the following:
If using non rechargeable batteries ensure that they are new.
If using rechargeable batteries ensure that they are fully charged.
That the battery terminals are clean and bright and that they hold the batteries snugly.
That the batteries are inserted with the correct polarity, (see User manual p4).
Try running it on a suitable AC adapter. Just "google" AC adapter for InnoTab 3 to find the right one if you don't have one. The adapter overrides the batteries.
If the AC adapter doesn't make it work and you have tried the above battery checks, unfortunately there is problem with the power circuitry within the unit.
It may be worthwhile to contact an electronics repair centre and get a quote for a repair.
Here is a link to the user manual.
If it turns on and stays on but it is not functioning correctly, here is a link on how to reset the unit.