Hmmm....could be old like you said. If it was in a good environment it shouldn't have any problems. The head unit only has outputs for two speakers? It "should" have two RCA type connecters coming out (one white, one red) and 8 total speaker wires coming out the back. 2 green, 2 white and I forget the other colors. Purple and grey I think. One of each color will have a black stripe for the negative. The amp should have two RCA inputs and then 4 total terminals, two positives and two negatives.
To run something in series, you'd hook up positive to negative. For example: If you have a flashlight bulb and want to get it to be the brightest possible, you'd hook the negative of the bulb to the negative terminal on a battery. you'd hook the positive of the battery to a negative on another battery and the positive of THAT battery to the positive of the bulb. If you were using two 1.5 volt batteries, now you'd have 3.0 volts since they're together. Clear as mud? Good.
Parallel means you'd hook all the positives up and all the negatives up together. You'd still only have 1.5v, but you'd double the capacity of the battery life.
In an amplifier situation, if you put all of the speakers in parallel, you'll draw more watts and amps from the electronics and possibly overload it. If you run the speakers in series, they won't be as loud, but it'll be safer for your setup.
Do you know if your amp is bridgable? That's a whole 'nother ball of wax...but a good one.
Someone else chime in here to explain things more clearly...my mind is split pea soup today.