hilukasz:
I have no problems running the chip, it really only has to do with serial output. I've gotten it to even output "PWN" (software on a few pins) on 5 pins, so it seems like it's pushing it hard. But I will check out the datasheet, I didn't think to check if it's outputting enough power for HIGH on arduino.
My suggestion could be a complete red herring, but easy to eliminate by running a sketch that just flips your TX line in a loop and looping with a digitalread at the Uno end. Will try it tonight myself to eliminate that possibility if you don't get a win first.
I make up these handy 1" square protoboards with a CR2032 holder, socketed ATTiny85, decoupling cap and all the legs broken out to headers...so likely have one of those that's not on Xmas lights duty to check this 
Geoff