Can you use any brand computer power cord on your laptop computer?

No, in most cases you can not do this. Most of the time the connectors are not the same anyway, but even if they are, it is still not advisable. Many laptop computers run on slightly different voltages, and some use more amps than others. If you use the wrong voltage/amp rating, you could damage your notebook. If you know for a fact that the output voltage, amps and polarity are the same, and the connector fits, then you should be OK. If in doubt, don't do it without getting some assistance from a professional.