It all depends on how long ago the suspensions were. I think you need to have you license back for a year before someone will seriously look at you. Also it depends on how long they were suspended for.
What were the issues, and have you gotten them taken care of? Is your license likely to get suspended for this again?
"non-moving violations"...let's see; parking, unregistered vehicle, what else would be "non-moving"(?)....could show a company that you have little regard for regulations. Actually minor infractions, and with the increased demand for drivers....probably be little or no problem.
Suspended license is one thing, having it suspended because you "forgot" to pay fines shows you aren't that responsible.
Will it hinder? Of course. But it won't keep you from getting a job if you do not let a few obstacles get in your way. It sounds like you were behind on Child Support or something. If that is the case then the suspension should not be a problem. I would take a copy of my child support payments to show they are up to date with you to interview. Also, get over yourself. Don't try to sugar coat things. Tell them up front that you got behind on Child Support and it caused your license to be suspended. We live in the real world and there are real problems that we have to deal with. Again, I am just assuming that is why your license was suspended. Turn it around and use it to your advantage. Tell them they can count on you being at work because you have child support to pay.
Nah! Driving someone's else's car with no insurance or inspection, thought they would pay the fines cuz I didn't have the bread. Anyway license got suspended, still kept driving got pulled over again for "no light on the licence plate" the rest is history.....