Does this speaker sound like it could be blown?

I wonder if you know what a "blown" speaker sounds like. If the HF is "blown," it will sound different from the situation with a "blown" mid or woofer. So which is it?

OTOH, if the issue is intermittent or level-dependent, it suggests an intermittent connection or cold solder joint.

I hate to ask a question to answer your question. Have you been listening to the speakers at loud enough levels to blow them? Most of us know the limits of the speakers we own and what volumes they are comfortable with. There is the point of loud where the speaker is working just fine without much risk of damage. Then there is the loud where you start to reach driver compression and distortion sets in and damage to the speaker starts. Have you exposed the speaker to the latter? Some people don't care to know and honestly cant hear when a speaker is reaching its limits. Im giving you the benefit of the doubt that you can hear and no when you are pushing a speaker to hard. The noise you are hearing, especially during bass heavy moments. Does point to a driver that is blown. One other possibility is that something has went wrong inside the speakers cross over. It could possibly have a weak solder. Not real likely, but it can happen. A part of the cross over could of become over heated and damaged if the speaker was exposed to loud volumes. There is usually protection for this but it's never a guarantee.
Also keep in mind that a speaker can be blown and only have issues at certain volumes or while playing certain frequencies. A blown speaker does not have to sound bad all the time, at all volumes, or while producing all frequencies to qualify as a blown speaker.

It has been my experience that a blown speaker doesn't play well at low volumes. You might have done some damage to the voice coil on the speaker if you had the volume up loud when there was a big explosion on the sound track.