So what I understand is that you installed CROMI-X rom on your TF300. If you press the buttons or you charge your tablet, you hear the sounds. So: your tablet is on.
What I would do: uncharge your tablet wait until your tablet goes off because of the zero battery level. Then charge your tablet again and restore the original version of your TF300T when you bought it (here, I guess
Then make sure you have the correct everything (drivers ...) installed.
I read this at the topic:
YOU MUST BE ON JB 4.2.1 WITH THE ASUS STOCK BOOTLOADER 10.6.1.8 AND TWRP patched 188.8.131.52 or BOOTLOADER 10.6.1.15.3, 10.6.1.27.1, 10.6.1.27.5 or 10.6.2.x and TWRP 184.108.40.206 BEFORE FLASHING THIS. THE BEST WAY TO DO THIS IS TO FLASH THE STOCK ASUS 10.6.1.27.5 or 10.6.2.x FIRMWARE.
If your 100% sure you have the correct bootloader, TWRP, firmware and drivers: reflash the CROMI-X rom.
I'm pretty sure there are other ways to fix this problem, but this is the only way I would do it.