I was a bit confused, sorry. It does not power on (you said) but rx/tx leds are on. So it must be powered on.
Is the board detected in the IDE? If not the TTL-to-USB is damaged.
If the board does NOT use the CH340 TTL-to-USB converter and it's detected in the IDE, you can run the loopback test; Loop-Back Test Instructions. If that fails, either the TTL-to-USB convertet is damaged or the 328P.
Does your Uno have the DIL 328P that you can replace? If so and your conclusion is that the 328P is damaged, you can buy a new one; life will be easier if you buy one with optiboot (the bootloader) preloaded
I have no experience with chromebooks so probably can't help further.