Using capacitance would be unlikely, as resistance is cheap and easy. It usually is as simple (row, column) as Brian has suggested. I worked on a project that was a bit more complex, in that the keypad had a separate chip that would encode the (row, column) output into a 4-bit value (i.e., pressing the number 1 was converted into "0001"). I doubt they use that in remotes, though. You may also be able to examine the output of the button portion to determine if something is stuck (perhaps one row/column is shorted). If one column is shorted, selection of a button in another column would mean that the encoder chip could not determine an appropriate column. With no buttons pressed, the output should be either low for all outputs (columns, rows) or high (columns, rows), depending on whether pullup or pulldown design is being used. Try to figure out which buttons work and what columns/rows they belong to.
Is there a reason why you want to fix this remote? Usually, one just buys a cheap "universal" remote when a remote breaks.