I'm not a member on the site. But I have made online purchases via credit card and PayPal from numerous online sites!
But the site does say they now accept PayPal!.
Are you logged into your profile?
Do you have a page that confirms what you have ordered and what the final price is with Shipping?
There should be a way to click on a link through your profile or by viewing a Shopping Cart to confirm your purchase and pay based on an actual totals given to you for shipping to your address.
Generally paying online, you go through a series of around 3 pages for purchasing.
Some sites will prompt for you to verify your user name and password again, despite being logged in.
The site will ask for a Shipping Address and Billing Address
Payment is usually the very last page of the transaction.
Also, some sites have you register a credit card or Paypal upon being a member. In doing so, it makes buying things easier because you may not have to fully type in a credit card number but you will have to verify that you want to use the selected credit card or a different one or Paypal.
It's also possible, that you may receive an email from the website, informing you that you have "won" an item and can proceed with a link sent in that email for completing the purchase!
Let me know if this is helpful! Otherwise I'll look into more resources.
Also you could email their Customer Service. Many websites have 24 hour or late night customer service reps for online transactions and website help.