I think you can open a seller account even if you don't have PayPal, so long as you meet the other requirements like how you will pay for your seller fees and offer safe payment methods other than PayPal. But you will need a verified PayPal account if you plan to open a store on eBay.
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Do take note that eBay and PayPal belong to the same company so if your PayPal account was limited or restricted due to certain activities on eBay, it might not be as easy. They may do a counter reference of your previous accounts. But may be worth the try!
Hope this helps. All the best :)