Yeah, some serious problems with the idea of using the shuttle to go to the moon/mars.
1. The SSME is not designed to be restarted. Getting a big turbopump like that going in space is a big challenge.
2. Assuming you take care of #1, you need to add ullage motors to the Shuttle/ET stack to get the fuel pushed down against the feeds until SSME thrust is high enough. You might be able to use the OMS for this, but you're going to have a real problem keeping the off-center thrust from putting the stack into a forward pitch roll.
3. There are no fuel carriers in the inventory for bringing liquid hydrogen and liquid oxygen in sufficient quantity up to refuel the ET enough to provide the impulse needed to go to the moon. You would need to create a new rocket designed to carry a heavy and bulky payload of fuel up (LH^2 takes up a LOT of space for given mass).
4. Assuming 1-3 is fixed, now you need a way to transfer fuel/oxidizer to the ET. There's no gravity, so you can't just pump it, and you'd need a system that wouldn't weigh too much or else you can't carry it up. Let's say that you dock with the ET stack and set up a slow spin so you use gravity to force the fuel/O2 down to the intake holes, and that somehow you've managed to create a method for pumping it from one tank to another. Better yet, assume that instead of taking the ET up to orbit, your fuel carrier is its own tank with the same locking points that can attach to the SSME right where the ET was, that way you don't have to do a complicated refueling.
5. Which brings us to another problem, getting the two to dock in orbit. There's no automation, not docking systems that are designed to do this. You would need to jack the two together and hope that someone can get between the OV and the tank to hook up the attachment points. I've seen that space, it's not very big, but it has to be hooked up strong because the SSMEs can't be throttled down very far, so it has to hold against many G's of thrust.
6. Assuming 1-5 is magically taken care of, now you have a small cabin attached to about 100 tons of structure that's designed to handle re-entry to the earth's atmosphere. You're dragging along tons of excess mass in the form of wings, heat shields, vertical stabilizers, landing gear, etc. For every kilo of mass you carry, you need like 10 kilos of fuel. So we're talking multiple launches of fuel tanks, each atop multi-hundred million dollar EELVs. The cost, at this point, it passing $5 billion.
7. Don't forget your martian lander. You can't just pull a lunar lander out of the Smithsonian, hook up a laptop to the control system and top off the tanks. You need a completely new vehicle. Since we're not doing Zubrin's Mars Direct, there's no fuel factory waiting for us on Mars, so the lander has to be able to carry enough fuel to launch back to orbit. One third earth gravity and lower air pressure, sure, but still, a lot of fuel.
8. Assume that 1-7 have magically been solved. You now have an environmental system on the shuttle that was designed for missions of up to a week, maybe as much as three weeks with the extended stay module. The shuttle uses fuel cells that convert liquid oxygen to power and water, so you need enough O2 go juice to last the whole trip. If you don't, then you're betting that your APUs and fuel cells will fire up again after months of cold soak. Hope you bought a lotto ticket, because if you live to check it, it's gotta be a winner.
9. Assuming 1-8 have resolved themselves. You need a method to aerobrake at Mars while holding onto your fuel tank. After all, you need to come back to Earth, right? So your fuel tank cluster now needs to have heat shielding.
I could keep going, but I have to get back to work.
PS, the cargo bay cannot be pressurized.
