UPDATE: Okay, so I couldn't take out the white base (I save before I tried, and got decimated) but my forward position has been set up at a mining position I just discovered, more defendable than the other one. After that, I started developing a fleet of 10 battlecruisers. Since my 24 or so siege tanks can easily protect my bases, that fleet is almost ready to move out, and with a couple of science vessels as detectors to ensure ghosts don't get the better of me again. Tomorrow night, I strike.
I believe I had developed a winning strategy for Starcraft, Episode I, Level 10, "The Hammer Falls".
1. Ignore the strategy guide. Yes, it has a nice map that tells you where the enemy is, and where you can place bunkers, but it's strategy is flawed.
2. Set up your base ASAP; make a barracks, 2 supply depots, a factory, a science facility, and a starport, as well as a ton of SCVs.
3. Set up your two tanks in defensive positions on the upper rim of your current base, (the only thing you should have researched is siege mode) with fully stocked bunkers and missile turrets close by. Start churning out siege tanks, and reinforce your marines until you have a decent amount. Get two science vessels to act as mobile detectors. Then, move out to the right and up to the first bridge; On the way there will be one or two goliaths, and a squad of marines.
4. Reinforce that area with missile turrets and bunkers guarding the bridge. Get as many siege tanks as humanly possible there and in siege mode, inching them forward when a new layer is complete. Make sure your science vessels are there as well, and get a couple reserve bunkers in the area you fought the goliaths in, just in case. When Alpha Squadron (White) attacks through that way (and it will) their force will be comprised of at least 2 goliaths, a bunch of siege tanks, and upwards of three cloak-enabled ghosts. Blow them to hell, and then move out, attacking their base instead of setting up a forward position in the mines. Once their base is clean, go to the forward position (leave a couple of tanks there, though, with a few missile turrets) and start setting up a base. Go to the upper side of the station, and set up a perimeter there; block of the bridge to the left, and make lots of missile turrets as resources allow. Then, start climbing the tech tree.
4. Churn out 6-12 Battlecruisers, fully upgraded, and make sure to upgrade your vehicles a fair piece too.
5. Send the Battlecruisers in to wipe out the enemy and yamato the ion cannon.
6. Victory! You, Jim, and your men are outta here!