I did not know they had an 80 watt version of that cpu, but If you look at the power supply, it seems to only list a combined wattage for the 5/3.3 lines. This makes the design older. It also makes it hard to know just how much 12 volt power the unit actually has.
You can NOT just add the 2 rails because in most cases they come from a single rail that is not big enough to drive BOTH at full power.
Newer power supplies push most of the power into a large 12 volt rail(leaving the rest for standby and other things). That rail powers most of the system and then DC-DC conversion uses a part of it to power the 3.3 and 5 volt rails. This means higher 5 and 3.3 voltage use will take some from the 12 volt rail, but it also means that the 12 volt rail has MUCH more power then older power supplies.
For example, and older Antec TruePower(once though of as VERY good) 380 has over 100 watts less(216 watts) then the newer Earth watts 380 watt power supply(324). By the same note, I have a 300 watt power supply(22 amps @ 12 volts or 264 watts) with more power then the old 380 watt TurePower 380.
In a nutshell newer hardware uses power differently then older hardware and as such, many times and older power supply(even a higher wattage one) may not be suitable for a newer system or hardware.
This site lists your power supply as having 20amps(MAX) on its large rail that feeds the 2 small rails. This puts your just within the general requirements.http://archive.unlimitpc.com/review/5_enermax/ATX%2012V%20Ver.2.0%20%20Coolergiant%20VHB%20P%20Series/Coolergiant%20VHB%20P%20Series.htm
I am not 100% sure how accurate this would be, but you see it is kind of close.