I'd have to say the symptoms sound exactly like old brake fluid with air and/or water contamination. It would not be a bad idea at this stage to replace the piston seals (I think that is what you were referring to), since all rubber parts will deteriorate in brake fluid that is old. Still, the seals themselves will not likely cause your problem - you need a complete system flush, and this also should involve an inspection of front brake calipers and possibly master cylinder if the fluid is really grungy.

Steve