What's wrong with my speaker?

Pressing on the driver can change the alignment while you press, and it can limit the travel.  You might actually try an ageing woofer trick. Put the speaker in upside down.  I have seen (i.e. heard) this realign a sagging suspension enough to cure the problem.

Either the voice coil is rubbing, or the speaker is traveling out of its intended  range of motion, or both  I once bught a set of B&W DM 14's which had tweeters substituted from a cheaper speaker.  They looked identical until I removed them. The popping and crackle at high volumes was because the cheaper speaker had a smaller voice coil and magnet, from a cheap B&W that cost a quarter of the DM14 price. You might be able to order a new driver, and on domes, replace only it, but you will not be able to straighten a bent (overheated) voice coil, unless you value your time at about a nickel an hour, or have a lot of experience, which practically no one does, because people value their time.