If you have a dmm I would check to see if the attenna is really connected to the antenna input behind the deck, sounds like it might not be.
As for the general shittiness of the sound, play with the fade and balance controls on the head unit to isolate each speaker, if all sound shitty then get a new head unit, if one sounds way worse / better then that's where you should look into...
I aquired the speakers used for free unless they are shot and I don't know it.
does this mean you are only gonna pay if they are shot ? j/k