You can certainly get your games back. The procedure depends upon where you purchased them, since every game site handles their own sales and game registrations. It's best if you can remember where (which game site, e.g. directly from LDW, Big Fish Games, Yahoo Games, etc.) you purchased the games from to make it easier to locate your purchase. The procedures vary from site to site, but this answer in our Support FAQ should help you get started.
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Barbara
Unicorn
Last Day of Work