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.
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Of course, Portals can also be customized, so removal and/or addition of features definitely possibile should you see fit.
Hope this helps.
- Justin