If they truly are PSA cards, you can submit them. They have a special on anything from 1996 to newer at $15/card (USD) as long as you submit 10 or more.
There are also lots of places that will do group submissions for you, and typically charge a small margin to allow you to submit fewer cards.
If you're looking at cards pre-2000s though, just keep in mind a PSA 10 is pretty hard to come by. Older cards almost always have issues with things like centering, edges, and surfaces, that you may not even be able to see.
There's a reason why an upper deck Ken Griffey Jr. PSA 10 rookie goes for $2000 despite the fact it's an ultra common card that goes for $50 ungraded. It's extremely difficult to find a copy that would grade a PSA 10.
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