The charger you go, is it aftermarket or OEM? If it is after market, it is possible that the charger isn't actually correct for the device. Yes, I know they advertise them as for a particular make/model, but there are a lot of cases where aftermarket ones wind up not putting out as much power as the device needs. So if that is what you got, I would really suggest returning it and getting an OEM one.
That said, the waiting 30 seconds is not meant for taking them all out (charger and battery) and putting back. Here is the correct way to try that.
Try the following and see if it will turn on.
1. First make sure the device has been charged.
2. Unplug your charger cord.
3. Remove the battery.
4. Press and hold the "Power" button for 30 seconds and see if the device will turn on.
5. If it does, great, if not yet, no big deal. Now plug back in the power/charger cord. (If it didn't turn on without the cord in, it should turn on once you it is in. Yes sometimes they will turn on, or try to turn on, even with nothing attached/plugged in.)
6. Now put the battery back in.
Should that not be the problem, then check the battery to see if it needs replacing.