Personally, I'd say that if the MCU was fed with 8V instead of 5V -- then that toasted it, for sure. They are absolutely not tolerant of such treatment, I'm afraid.
Evidently, the Flash ROM and EEPROM circuitry can stand it -- which does make sense, given their internal operating nature. But I feel certain that the CPU circuitry would have been utterly destroyed by the over-voltage. (It would only take a single sub-circuit to be damaged to render the chip inoperative, after all.)
Do you have what is needed to remove and replace the chip? The safest way I know to do this is to pre-heat the board from underneath to 150ºC. Then use (maximum) 360ºC air from above to melt the the solder and remove the chip. Obviously, a suitable hot-air set-up is required.
You can get away with only 360ºC air from beneath the board IF you are very careful and VERY patient. This temperature is hot enough to damage the PCB if concentrated on a single area for too long -- and it takes at least four (4) full minutes to get enough heat through the fibreglass to melt the solder above.
I can report that I have several times moved an ATmega2561 (64-pin version) from one board to another and not had any trouble with it afterwards. So I believe it's far less likely that heat dmaage is the cause of your problems.
If the above is not going to be practical, I can offer to attempt an exchange for you, if you post the board to me. HOWEVER, it is very easy to damage the finer tracks of the 100-pin ATmega2561 and I have failed to do this without damage on one out of two occasions in the past. So I can only offer to do my best. (I will provide the replacement chip for you and return shipping, regardless of success or not.)
Good luck and do report back.
Bryan.
many thanks to Cam and Romolo for your responses