Can't Access Titan Weapons
You should be able to click the Buy Now button, then the Proceed To Checkout button. TW should cost 0 Points, though it will say 800 until you get to the Shopping Cart screen.
If that's not working, load up the Beta server. AFAIK, it still works fine there.

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I'm in the same boat. I've tried all manner of different approaches to purchasing TW on the beta server, none of them are working. I get the exact same behavior and message as OP.
Same issue here. Interestingly, there are two different Beta server options.
On "Beta Server", I have no points and no way to get more.
On "Beta VIP Server", I can't log in at all... on this VIP account... so, I don't know.
Has anyone else been getting that?
EDIT:
Thanks for the info, Kheldarn! It looks like I missed a step - providing credit card info to "buy" points.
The only remaining issue that I can find is that Titan Weapons isn't on the powerset list so it wouldn't be "purchasable".
Currently playing:
Infaerna Who knew Fire/Fire Brutes were fun to play?
Ignore the Beta VIP Server. Nobody can log in to it, and it's now misnamed.

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I really wish the server techs would rename these servers, this is becoming the Question of the Week, not that it's the fault of the newer players involved.
Thanks for the help, everyone. Everything went fine on the Beta sever. The test server is still not letting me buy the set, but at least I can play it now. Thanks again!
Nice! For anyone else having issues, if you can catch @Alpha Wolf 2 on the Beta server, he can grant you Titan Weapons.

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Hello everyone,
This is my first time trying out the test server, so I apologize if this is a known problem. I've got test server access set up and can create characters without issue. However, when I try to go to the Paragon market and buy Titan Weapons, I have no points available to purchase anything with. I've tried buying the set anyway, but no discounts are applied and my only options are 'Add Points' or 'Continue Shopping'. Clicking 'Add Points' generates an error to the effect of 'The Beta Billing and Account Management services are not available at this time.' For the sake of completeness, I did check to see if the set was simply available during character creation. It is not.
Am I missing a step somewhere, or is this a bug?