You have kind of narrowed down the issue and as other components work on another motherboard and the motherboard is showing symptoms of being faulty with another PSU I'd say it is probably damaged. If you can take it to a local service shop or something like that to make sure if it's got a problem.
As for a PSU I'd say get the best quality based on your budget-bracket. Consistency and longevity of all other components is directly related to the stability and 'cleanness' of the electricity provided by the PSU.
Yes proper grounding (if done properly) should in fact protect devices against surges and spikes and such. But that, here, would actually to a large extent apply to the PSU itself being vulnerable to such events. As I said, whatever happens on the AC mains a proper PSU must be able to protect components that are connected to it's DC output. You can protect your PSU, and therefore your PC, by using power extensions that have proper AC Surge protectcion implemented in them.