You didn't need to bleed them. The hydraulic system is closed, so if you don't take the lines off, and there is no evidence of leaking fluid around the piston, you don't need to bleed because there's no way air got in.
So yeah if you broke off the bleed screws you will need to replace the calipers and bleed the system. If you've never replaced the fluid before, it's a good time to 'flush' the system by pumping at least two quarts of new fluid all the way through the lines to all four wheels.
Get a helper to pump the brakes while you crack a bleeder into a pan (or install one-man "Speed Bleeder" screws - they're about $25 a set). Pump until the master cylinder is ALMOST empty. DO NOT
let it go dry and suck air, because if air gets into your antilock valve, you're fucked - that requires a trip to the dealer to bleed. Refill the master with fresh fluid and repeat the process. By the time the master is just about empty again, you should be pumping new clean fluid out the bleeder. Close that one, refill the master again, and repeat at the next wheel. Repeat for the rest of the wheels.
Old fluid CAN cause sponginess due to absorbed water.. But that will not 'just happen' when you replace the pads/rotors. It builds up gradually over time.
The sponginess you have is from not properly 'bedding' the pads to the rotors. There is a good possibility you may have wasted the pads, and you will have to eat it and get new ones again. You will also have to re-sand the rotor faces to remove any imporper glazing and start again with a clean surface. BTW, even brand new rotors must be sanded before installation to remove the protective lacquer that the factory puts on to keep them from rusting in the box.
Here's the bedding-in procedure:
When following these instructions, avoid other vehicles. Bedding is often best done early in the morning, when traffic is light, since other drivers will have no idea what you are up to and may respond in a variety of ways ranging from fear to curiosity to aggression. A police officer will probably not understand when you try to explain why you were driving erratically! Zeckhausen Racing does not endorse speeding on public roads and takes no responsibility for any injuries or tickets you may receive while following these instructions. Use common sense!
* From 60mph, gently apply the brakes a couple of times to bring them up to operating temperature. This prevents you from thermally shocking the rotors and pads in the next steps.
* Make eight to ten near-stops from 60mph to about 10-15 mph. Do it HARD by pressing the brakes firmly, but do not lock the wheels or engage ABS. At the end of each slowdown, immediately accelerate back to 60mph and then apply the brakes again. DO NOT COME TO A COMPLETE STOP! If you stop completely and sit with your foot on the brake pedal, you will imprint pad material onto the hot rotors, which could lead to vibration and uneven braking.
* The brakes may begin to fade after the 7th or 8th near-stop. This fade will stabilize, but not completely go away until the brakes have fully cooled. A strong smell from the brakes, and even some smoke, is normal.
* After the last near-stop, accelerate back up to speed and cruise for a while, using the brakes as little as possible. The brakes need only a few minutes to cool down. Try not to become trapped in traffic or come to a complete stop while the brakes are still very hot.
After the break-in cycle, there should be a slight blue tint and a light gray film on the rotor face. The blue tint tells you the rotor has reached break-in temperature and the gray film is pad material starting to transfer onto the rotor face. This is what you are looking for. The best braking occurs when there is an even layer of of pad material deposited across the rotors. This minimizes squealing, increases braking torque, and maximizes pad and rotor life.
After the first break in cycle shown above, the brakes may still not be fully broken in. A second bed-in cycle, AFTER the brakes have cooled down fully from the first cycle, may be necessary before the brakes really start to perform well. This is especially true if you have installed new pads on old rotors, since the pads need time to conform to the old rotor wear pattern. If you've just installed a big brake kit, the pedal travel may not feel as firm as you expected. After the second cycle, the pedal will become noticeably firmer.