Welcome to Android Central! After powering down, try powering up again by pressing and holding the Power and Volume Up buttons--keep them down until some kind of recovery menu appears. If that doesn't work, try Power and Volume Down.
Let me elaborate on that, this will open the bootloader menu. Once in that menu, look for the option that says "Factory Reset" and a "Wipe Cache" option. You can navigate the menu by pressing the volume keys. Also, do remember by doing this you will be wiping your Asus Transformer CLEAR of all personal data that is stored in the internal memory of the tablet! If that doesn't help and you are still stuck in a bootloop, I'm sorry to say but then you will have to flash in a new ROM on your device. For that you will need a custom recovery (I suggest TWRP, you can Google TWRP and go to the first link and just find the recovery for your device, they even teach you how to install the recovery). Once you have done that, you can find a custom ROM for your device or even the factory image online on XDA developers, Clockwork Mod, CyanogenMod or searching for the factory image (the default ROM). You can download the ROM and flash in via the custom Recovery by going to the bootloader again (Restart while holding Vol. Down) Then selecting Go to Recovery Menu (pressing Power + Vol Up once the exclamation sign appears, alternatively if you have any experience with how to use adb you can simply use "adb reboot recovery" as well). From there, simply flash in the ROM from the "Install via .zip file".
Facebook
Twitter
Instagram