Integrated forum, blog and cart shop

Hi,

I've got a potential client and potential problem. The client wants a
website based on CMS with forum, blog and cart solution. Here's the
problem.

I could offer him:

- website based on CMS, e.g. joomla
- blog based on wordpress
- forum based on vBulletin
- and shop cart based e.g. on cubecart

The problem is I don't know ( and I assume it's rather not possible )
to integrate all of them into one website with the same look ( which
the client could stomach ) and, what's the most important, the same
login and password for the user who could access forum, blog and cart
shop.

Is there any solution or any way to integrate all of the requirements
into one?

...or bespoke solution is the only option?

Cheers,
Richard