laptop battery cells measurement
What you are thinking of doing has been done successfully a lot of times.  FIRST, read the answer above carefully, if you do not understand the li-ion batteries, do not do this, but if you are ok with li-ion then it can be done quite easily if you have the right tools.

Most people will very carefully dissamble both laptop batteries, being careful not to destroy the battery management system.

Measure each individual cell's voltage, if any cell is less than 3 volts, it is no good and don't use it.  Any cell that is greater than 3 volts, is likely ok.  This is where having the right tools is nice.  If you have a fancy li-ion charger/discharger, you would then charge all of the "good" cells fully and then discharge then and measure their capacity.  Take all of the cells with the same capacity and put them together the way you found them to make one laptop battery.

Another way is to fully charge both laptop batteries, then fully disassemble them carefully.  Find something electric like a toy or LED lightbulb that you can use to connect a cell to discharge it and time the discharge.(Be careful to measure the voltage of the cell periodically to make sure that it doesn't below 3.0 volts when doing this).  The cells that took the same time to discharge will be of the same capacity and ideal for rebuilding into the one laptop battery.  The bad cells from each of the laptop batteries will likely discharge very quickly or almost immediately, so it should be easy to find the bad cells in each of the laptop batteries and discard them.

Be careful when rebuilding the laptop battery that all the connectings are the same as when you disassembled it.

If you do it right you will save yourself from buying a new laptop battery!  good luck!