One speaker buzzing when turned on, others are fine

My rear deck speakers were going out so I got some new ones about 2 months ago and installed them - Sony 6 1/2. The left rear was then fine, but the right rear was still cracking a bit. I had also been having some trouble with the head unit (old Pioneer) so I got a new head unit (Sony Xplode) and just installed that. Now, the right rear speaker works fine, but the left rear speaker, which was fine before, will buzz or hum for about 10 seconds on start up, then no sound at all from that speaker. I start the car, the left rear speaker buzzes for about 5-10 seconds while the other speakers do nothing, then the left rear speaker stops buzzing and the right rear and front speakers start playing music. The head unit displays "failure" which the manual says indicates that there is something wrong with the speaker wiring or connection. I thought maybe the wires needed to be replaced before this, but I didn't do anything with the wires and the right one didn't work before the head unit but the left did, and now after changing the head unit, the right one works and the left doesn't. What gives?

sounds like the bad speaker has been grouded out to the frame somehow. Do you have another speaker you can connect up to that wire ?

Well last night after posting I pulled the wire off the speaker not working and put it on the right speaker. I had the volume turned down really low, so that I had to be right there to here it. It worked fine through that speaker. Then, I put it back on the "bad" speaker and it also worked fine. Then I connected the right speaker again and both were working fine. Then I turned the music up and the left speaker stopped working again. This time I left the music up higher, moved the wire from the left to the right speaker, and it did not work on the right speaker either. So does that mean it is the wire? I don't understand why it would work at low volume though...

then you have either grounded out the speaker wire somewhere or the amp in cd player is bad.