My CPU is running slow after a system restore (4x0.8 GHz). Turbo Boost is definitely not working. And how can I fix it?
Using the Intel power gadget (above) shows your CPU running at low speed.

In normal case that would be fine if there is no load.

I have MBA with 1.8 GHz Intel Core i5 and runs at 0.85 at normal use, how ever it does spikes to 1.8 + under load.

Since the computer processing speed depends on more than one factor (CPU +SSD read/Write+RAM)...

I would say you (your mac) is a candidate for the Apple Hardware test.

UPDATE:

If you have faulty battery (as reported by your hardware test based) then your Mac will automatically limit the CPU speed to about 1/2 (as designed by Apple.)

So fix the battery and you good to go.