The GFCI Circuit has gone haywire

[HandyDan]

I was getting ready for our Labor Day ten day trip.  I was vacuuming the carpet in the Holiday Rambler when the vacuum just quit.  I thought I had blown a circuit breaker so I went and recycled all the breakers.  That didn't fix anything. I check all the 110vt outlets and most of them had no power.  All the outlets on the GFCI Circuit were out, that is three outlets in the bedroom, one in the bathroom, and the outside outlet.  A little experimenting with the multimeter showed that there was power going into the breaker and if I bridge the black output wire off the breaker to the neutral bar, I had power there.  But if I bridge the black and white output wires off the GFCI breaker I wasn't getting anything.  My thinking is all these outlets are wired in series and if there is a break in the circuit, they all go out (even though the breaker is set). 
I thought I would pull one of the outlets out and take a look at the wiring.  I discovered the outlets have no screws.  I literally pried one out of the wall.  I have never seen any outlets like these.  They have romex cable going into and out of each end and no way of seeing how the outlet is wired.  I can't pull it far enough out of the wall to really look at the back side.  Again, I have never seen anything like this. 
I need some ideas on where to go from here.  Where should I look to find why the power is off?  I took a picture of the spaghetti mess behind the breaker box, but there are no 110vt connections there.  The cables just disappear into the walls or floor. 

[FrankenHome]

HandyDan, I know you said that you bridged the wires at the GFCI but the did you check for 120 v to the GFCI using a volt meter? If not I would do that first just to make sure you have power or not to the outlet. If you do then you know it's the GFCI. If not then your panel breaker may be bad or there's a problem with the wiring at the panel. Good luck.

[Rickf1985]

If those outlets are what I think they are they used them in mobile homes in the 70's. The wires go through and it gets pushed into a "V" blade which is the contact for the outlet. That is all the connection is is a cut in the sides of the insulation! I replaced all of them in the mobile home I was living in years ago, they are a safety hazard! They would lose connection over time from wires being plugged in and out and the cutting blades came loose. Then you had an arc and poof. I am not completely sure what you show is the same but it sounds the same from your description. Losing connection in one would not cut out the entire circuit though, just that one.