Move your troops west, attacking the hydralisks and zerglings you encounter. When you reach the base you will assume command and will also see the location of the Norad II. You have control of the forces there and should immediately put the marines into bunkers and repair the Norad and the bunkers there. Back at your base begin the preparations to save the Norad immediately. Unfortunately this means building up an economy (I recommend 8 on minerals and 2 on gas). Get units into the existing bunkers and build another one in the northeastern area that is undefended and stock it with units (each bunker should have 3 marines and 1 firebat). Since you can now build goliaths you should definitely do so. Also you can build the armory now which allows you to upgrade your mechanical units.

Once things are running smoothly your top priority should be upgrading the range of your marines as well as their attack as it is the best thing you have defending the Norad at this moment. Also you should consider placing at least one of the SCVs near the Norad into a bunker so it can perform repairs should the Norad suffer heavy damage. When you finally have all the structures built and are ready to start pumping out units here's what I recommend:

Send one vulture (NOT RAYNOR!) toward the norad to see the path you need to take to get there. That is to the northeast. The forces I took were: 12 fully upgraded marines and 6 fully upgraded goliaths. The marines should use the stimpack ability and go berserk on the sunken colonies you encounter. Your goal is to cut a path for your forces to take to get to the Norad. The goliaths are well armored and can support the marines very effectively. Cleave your path to the north destroying as many buildings as you can. When you have a moment build reinforcements at your base. You're not going to make it to the Norad II with the initial group but you will likely cause some lasting damage that will lay the groundwork for victory. I built the exact same group again (replaced as the first one was dying) and continued the attack. The transition was almost seamless and finished off the first base. Head to the east. You're going to go around the raised area of land the Norad II is surrounded by and come to the eastern side of the map. You'll likely be attacked by sunken colonies and even some mutalisks on your way. Destroy the latter but ignore the sunken colonies for now. You'll eventually come to a ramp. Take it up and you'll be very close to the norad.

Deal with this just like you did the first base. Do as much damage as possible. Stim packs work great here. Just focus your attacks on the sunken colonies. They're Priority 1 but you will also need to remove the spore colonies as they will attack the dropships you attempt to send to the Norad with Raynor. When you've basically wiped all the blue off of the southeast corner of the map you're free to send Raynor and the dropships to the Norad II.