Ah, re-reading it seems like one of your chains is not producing any power.
It looks like each row of 9 cells is wired in series. Further, rows are then wired in series so that every cell is wired in a big long series circuit. See if you can find a wiring diagram on the panel somewhere to confirm this.
Thus, with each cell contributing about 0.5V, each row should produce 4.5V. 4 such rows should get you to ~19V (with some variance due to load etc).
Now, when you have a cell in series with others and you shade it, or corrode its leads somewhat, it not only stops producing power, but it also cancels another cell out as it acts like a diode (see my last post). It looks like you have some wiring issues or something.
Try the single-cell shading thingy I suggested and see if you can identify which cells are producing power and which cells aren't. Hopefully it should be fixable with a soldering iron.
If wiring or leads are bad, short circuit current will be lower than rated or no current will flow at all. 9 cells will have to be shaded to drop voltage to 10 volts. Also 36x4x4=576 and 30x15=450.