This link says that web incidents are supported at the Free level, however, when I try to open a case using the web support at I am presented with the form below to fill out... and I'm unable to proceed.
How do I, as a consumption user, not a MSDN user, get free web support?
At free level only support for billing and subscription management-related issues is available.
So if you selected a category other than billing or subscription at first step, it will not allow you to submit a request without a support plan.
If you're looking for technical support your best bet is to submit your question here on stackoverflow or msdn forums; or buy a support plan.