Production : If the issue you're facing is in the Production, then you could log a case here : https://help.salesforce.com/orgpicker
Developer sandbox : Developers can get support by logging a case in the Production org and providing the ID of the sandbox.
Free Dev org : I don't think Salesforce provides support for free Dev orgs.Free Developer orgs do not show up under Select your org. Here is an open idea for enabling logging a case for Free Dev orgs
https://success.salesforce.com/ideaView?id=0873A000000lGplQAE&sfdcIFrameOrigin=null
I opened that page and selected the most obvious options, however the "Log a
Ticket" button stays grayed out. Am I missing something?