Hi Meghan,
What you could do here is ask the user if they're already a customer/lead (ex. "Have you contacted us before?"), then have logic on your website that displays your Web-To-Lead form or a Contacts Portal login depending on their answer.
Using a Contacts Portal, the user can login and open a Customer Service Case to ask their question. As an added bonus, they'd also be able to see any Recent Transactions or Solutions that have been entered.
Of course, Portals can also be customized, so removal and/or addition of features definitely possibile should you see fit.
Hope this helps.
- Justin