I do not know about unverified paypal accounts because i guess its same in every site the payment processes. Anyways you can use godaddy or enom for domain and for cheap you can use namecheap or maddogdomains.
you cant make payments with unverified paypal. There is just no way.
Godaddy is a cheap solution to buying domains. There are plenty of coupon codes which give you good amount of discount. I bought mine for 1$. but that coupon has expired.
Look around (google) and you will find some other coupons.
Yes Nuclearrambo is right. There are good number of sites which help you in buying domains. If you are purchasing hosting, some top hosting companies provide you the website free for life.
But go for godaddy.com, but they don't accept unverified paypal. Buy with your credit card directly if you have
Google for coupons, godaddy, namecheap, enom (I think that's the name), 123-reg and a few other sites offer cheap domains ($10 or less). I'm not sure which will let you use an unverified paypal but just look around.
Another really useful website to purchase domains from are netfirms. I bought my domain from there and they always have good support. You need a card though.
About the unverified paypal, you can purchase domains through namecheap without a card and unverified paypal, as long as you can send the money, it's pretty easy from there on.
Well Kill4, you could use ChromeWolf's service down there a few forums down to verify your PayPal. The only problem is, you just have to make sure your PayPal is atlest about a month old.