Are there any general-purpose programming languages with classes, objects, methods, interfaces, and so on, which disallow class-based inheritance?
This reads very much like a description of VBA - Visual Basic for Applications, embedded in Microsoft Office and other VBA-enabled hosts (e.g. AutoCAD, Sage 300 ERP, etc.), or even VB6. The "A" of "Basic" stands for "All-purpose" anyway, so there's the "general-purpose" part.
VB6/VBA has classes (and therefore objects), methods and interfaces - you could define an
ISomething interface in a class module like this:
Public Sub DoSomething()
And then have another class that does this:
Private Sub ISomething_DoSomething()
Such a class, exposing no public members, could only ever be accessed via its
ISomething interface - and there could very well be dozens of different implementations of
ISomething out there, so OOP VBA code is perfectly capable of polymorphism, and it's perfectly legal for a given class to implement multiple interfaces, too.
VB6/VBA does not allow class inheritance however, so you can't inherit an implementation from another type, only its interface. Now, whether this is an accident, a design flaw, a stroke of genius or a huge ugly oversight is open for debate; it's not clear whether VB6/VBA takes this to heart, but it most definitely enforces it.
If Go doesn't do class inheritance and is nonetheless an OOP language, then I don't see why VB6/VBA couldn't be considered an OOP language as well.