Asus tablets normally take much longer the power up if they are connected to the charger. Unplug the charger. Press and hold the power button or 5 to 10 seconds. If it does not start up it's possible that you discharged the tablet too far. When a tablet is discharged until the battery is flat often the charging circuitry will not function correctly, thinking that the battery is charged what it is not.
When this has happened it is necessary to make multiple attempts at charging it for between 30 and 60 minutes each time, unplugging the charger from the tablet between attempts. Sometimes it's possible to trick the charging circuitry, by plugging the USB cable into the USB port of a PC that's powered on instead of the Asus charger. The last option requires some tech expertise since you have to open the tablet and short out the battery for a minute or two. This can't be done through the charging port.
If you get your tablet to function again take care to not let its charging state drop below 10%; you're asking for trouble if you do so.
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