Unstable readings in photoresistor matrix with Arduino, OK with Ohmmeter - what's wrong?
The answer JustJeff gave you is probably correct for why you only get something when the ohmmeter is connected.  I'd like to address a different issue.  That issue is that your photoresistor array isn't going to work.

The problem is that you cannot "turn on" a single row at a time.  For example, lets say that you turn on the middle row.  The top and bottom row lines are tri-stated from the uC.  Current will go from the middle row line, through P5 to the left most column, through P1 to the top row line, through p2 to the next column line, and mess up your measurements for that column.  Now imagine lots of "false paths" and you can probably work out that everything will get hopelessly messed up.

One solution to this is to put a schottky diode in series with every photoresistor (with the diode "pointed" to the column lines).   You read a row just like you do now, although you might try driving the "unused rows" with a low signal instead of tri-stating them.  I'm not sure if you'll have some wacky leakage current issues if you don't. 

Even without the diodes, however, I would have expected you to read at least some voltage.  Your low-side resistors (R in your schematics) might be too low of a value.  Do like JustJeff said and measure the voltage on a column line.  If it's close to zero then you have a hardware problem.  If it's not close to zero then you have a software problem.

P.S., I didn't look at your C code, since I'm not familiar with programming on the Arduino.