I also had pins and needles and numbness when riding for more than half and hour. The problem completely went away when I swapped the flat handlebar for a different type of bar.
First I changed to a North Road bar and then to a drop bar. The advantage of the drops is the choice of hand positions and the ability to change position while riding.
The North Road bars I chose were slightly too wide for me so they're now surplus to my requirements and I'm selling them here. If you're switching to a North Road bar, you may need a longer stem in order to maintain a similar riding posture, due to the back sweep.
General cycling advice ( NOT technical ! )
I have only ever used straight bars on a kids bike and cant understand why they are so prevalent what with only one hand position and thus body posture. I dont think I could ride bike very far with them without wrists or hands suffering