You can probably skip the solder-sucking step and go straight to resoldering (with fresh solder). There aren't that many joints, so you can refresh all of the usual suspects in a short time. Just work carefully, and inspect along the way, to make sure that you have not created solder bridges. If you do, that sucker will come in handy to clean things up.

Also, do not overlook the connectors. The yoke connector is notorious, but it's also advisable to clean the terminals of the other connectors, too. These simple steps have fixed a great many otherwise dead Macs. I hope you are as lucky!