trouble is the cost - to check the CPU you need another working motherboard and vice versa.
plus your time added to the cost.
as its a afriend - you can probably go the extra mile - but the fan speeding up and down and the lack of regular booting noises indicates either or both MB and CPU are 'brown bread' (dead) as we say in cockney rhyme. you have to tell your friend in your opinion what you believe and suggest if they take somewhere else to get a quote.
Once I have tried a new power supply some spare ram then I suggest that the hard disc is housed in an extra enclosure and they buy a new PC and I transfer across the data.
if you take in to account the hours spent debugging the problem and the potential problems if it fails 2 weeks later or if you damage any new items you try.
one final thing...
for the motherboard - look at the capacitors (round cylinders) on the motherboard are the flat topped or bulging - see
http://www.thenakedpc.com/dan/Bulging_Capacitors/index.html