A possible explanation as to why you cannot find a CMOS battery explained here by John_295 thanks to Rustys for sharing this info with us
So, if this is the case with your model of notebook removing the main power brick + the AC adapter and leaving disconnected for a while would have the same affect as pulling a CMOS battery.
I know you said that when powered up the notebook shuts down after a few minutes but when you are next able to do this can you place the back of your hand by the notebooks exhaust vent to see if the air being expelled by the cooling fan is warm, if it is it suggests that there is power getting to the CPU, if it stays cold after restarting the notebook a few times it may suggest the opposite.
So, if this is the case with your model of notebook removing the main power brick + the AC adapter and leaving disconnected for a while would have the same affect as pulling a CMOS battery.
I know you said that when powered up the notebook shuts down after a few minutes but when you are next able to do this can you place the back of your hand by the notebooks exhaust vent to see if the air being expelled by the cooling fan is warm, if it is it suggests that there is power getting to the CPU, if it stays cold after restarting the notebook a few times it may suggest the opposite.