Shocks How to tell if they are bad!

I have a 1988 base convertible with 71000 miles which I owned since Oct 2016.  The ride is great on a nice smooth road and you pick up every imperfection on some roads but when you come across a major hit it is like the whole car will break in pieces and it like throws the car off track!  I can not move these shocks by hand is that an indication of a problem, I am 75 my friend has a 1982 and he has replaced his shocks and it rides about the same.  I can accept a stiff ride but what feels like the whole car is about to disintegrate is scary. The springs seem ok ball joints are good and I have a new rack.  It has acted this way from when I purchased it.  I have the blistine  shocks they were dirty at bottom but no wet areas. Will new shocks of the same brand solve this or go with another brand. I love this car on a nice smooth curvy road giving it a little extra gas through them.

Thanks for any feed back.

  Hi.  Are you aware that Bilstein will rebuild those shock absorbers?  I would first go to their website and read about this service, even email them about your concerns, and review their reply  before proceeding further.  The Z-51 option is stiffer, and I am presuming that your car is so equipped.  I suppose someone could downgrade that stiffness, but ultimately those shocks seem to be bad. 

Thanks for the info I do think that they are bad. I would go with the same shocks. I have an honest mechanic that would replace them for a reasonable labor cost. Take care!!!