You most likely have very old brake fluid in the system. Remove the cover on the reservoir and observe the fluid. If the fluid is greyish in color with bits of black stuff, like pepper, you have a system that must be overhauled. Your hoses are most likely deteriorated internally and have polluted the system and have now blocked certain important areas of the system such as the distribution valves within the rat trap. Once blocked they will prohibit and block brake fluid and act as one way valves and will not release until the system is drained and overhauled.
How far back did you have to push the pistons into the caliper to get the new pads in? It is very likely that the part of the pistons that has been extended past the caliper bore seal as the previous pads wore down has become corroded over time. Brake fluid attracts moisture from the atmosphere, even with a good dust seal moisture will get into the area under the seal and corrode the extended portion of the piston. Now that the corroded part has been pushed back over the bore seal, they have jammed there because of the corrosion and will not release when pressure is taken off the caliper. The piston is pulled back along with the brake pad simply by the flexing of the bore seal., so a deteriorated bore seal will also not flex to pull the piston and pad back away from contact with the brake rotor so the brakes will stay engaged. Have you checked to see if both front and rear brakes are locked? The other scenario that can happen with the early cars is that after you pry back the caliper pistons and replace the pads, the first pump of the brake pedal will travel much further that it has before because of the space created for fluid to travel when you pried back the pistons. When the piston of the small master cylinder gets bottomed out from the excess travel it can stick fully on if it is not in good operating condition. This will lock up the rear brakes, and also the fronts if one of the distribution valve plungers sticks down too. Often the rubber dust boots on the distribution valve plungers has rotted off, and the exposed part of the plunger rusts badly and will jam when forced past its normal amount of travel.
If the pistons have been forced back as Jim describes, with the rusted part now inside the cylinder, the only way to get them out may be:-
1) to remove them from the car,
2) block all the fluid holes except one,
30 drill right through a spare bleed nipple,
4) screw that tight into the last hole,
5) fill a high pressure grease-gun with grease,
6) force grease into the unit till the piston moves.
PS. hydraulic system problems are a frequent feature of elderly Shadows (and they are all elderly) - they are misunderstood and get the wrong sort of maintenance or none at all. Be prepared for a complete brake system overhaul, and look in the online literature for lots of hints, diagrams and help on the subject.
Hydraulic system failure can occur on anything with hydraulics due to lack of deferred maintenance,
No need to drill out anything.(spare bleed nipple?) and destroy anything. Compressed air or using grease will usually get the job done. Try compressed air first since it is easier and most likely more available.
Note: remove the pads and place a rag between the caliper piston and rotor. It will fly out..
Better to use this tool, reserve the grease method for badly seized pistons that cannot be removed manually. This will remove all but the most badly seized pistons, without the danger of using air pressure. It's described as a piston popper, or disc brake caliper piston puller or remover. If you pushed the pistons back and they moved far enough to get new pads in this tool will remove them.
Jim, I'm curious as to how this tool works and have always relied on air to pop 'em out. The jaws go into the piston cup and you basically wiggle the recessed piston out? I have never seen one of these.
Yes, the threaded part uses an Allen key to open the jaws which grip the inside of the piston. That gives you leverage to twist the piston back and forth while pulling up on it and it removes all but the most seized pistons. I've never had the need for grease removal on any running car that has come in with stuck pistons. I've only needed to use the grease gun method when I've bought core calipers that have been sitting around open to the atmosphere for years. I think it's a Lisle brand, but I can check today for you.