It is highly unlikely that the computer was damaged. It sounds like your fusible link has burnt out. There are two parts that typically fail when jumper cables are reversed. One is the fusible link; which is a specially designed cable between the battery and the firewall. It is designed to burn out if jumper wires are reversed; and thus prevents the car's electrical wiring from catching fire. It may look like any other cable; but it usually has an identifying tag on it, or it is a different color than the other wires. After you buy a new one; it will then be easy to locate it on the car, by comparing the new part with the cables that are on the vehicle.
It is a good safety practice to disconnect the battery ground cable before doing any work on the vehicle's electrical system. That way; if a wrench you are using to tighten a bolt on a hot wire happens to touch a grounded object; there will be no bad consequences.
The second part that often fails is the alternator. If the alternator diodes have shorted as a result of the reversed cables; this will destroy a new fusible link as soon as you reconnect the battery after installing the new link. In order to prevent this from happening; the power wires to the alternator should be disconnected BEFORE you install the new fusible link. After the new fusible link is installed, you can check to see if the alternator is damaged by connecting the battery, and very quickly and lightly tapping the power wire to the alternator terminal where it normally is attached. If there is a spark, immediately pull the wire away; and then replace the alternator. If there is no spark, the alternator has not been damaged, and you can hook the wiring back up.