The reed contacts are normally open.
Let me give you the basics on what it's doing and why it's there.
People wanted to make their HP41's faster.
The HP41 has an internal oscillator that determined the speed at which the calculator runs. By changing the value of one component (reducing the value of a capacitor) the oscillator will run at a higher frequency, and the calculator will go faster.
However, some peripherals (notably the card reader) may misbehave if the clock speed gets too high. This generally manifests itself in cards that cannot be read in other machines.
But some people still want the calculator to go as fast as possible, and want to slow it down to write cards. To do this, the calculator needs to run at 2 speeds, a higher one to run programs, and a lower oe to write (and possibly read) cards.
To have this 2 speed arrangment, one possibility is to replace the capacitor with one that allows the calculator to run as fast as possible, then to switch in another caacitor in parallel with it for slower speeds. (Notice that capacitors have a higher value when placed in parallel, which is exactly the reverse of what happens with resistors).
Without having seen your calculator, this sounds like what was done and the method that was employed.
Although there are exceptions, the reed realy is open without a magnet nearby. Thus a broken reed relay is either going to give you the fastest speed (if it remains open) or the slowest speed (if it remains cosed).
However, it is possible that the original value chosen for the smaller capacitor (for higher speed) could have been arginal (which is pretty much the idea :-) and the oscillator no longer oscillates, or that the calculator can no longer handle the speed. In this case, removing the broken reed relay and replacing it with a link will give you a slower (but working) calculator. And you'll probably be able to use the card reader on it.
It is also possible that the wiring of the additional components was a little dodgy and that wires have come adrift leading to problems.
It is also possible that the calculator was damaged during (or after) modification, and you have a faulty calculator beyond the broken reed relay.
If it were me, I'd try using a link, and if that worked, I'd get a new reed realy and play around with capacitor values until I got a calculator with the two speeds that it was originally modified to have.
WARNING: If you're going to use a soldering iron inside an HP41, please:
1) have experience soldering
2) use something with a fine tip (or wrap thick copper wire around the tip and use the end of the wire as a tip)
3) turn off the soldering iron before you start to work on the calculator (unless you know your iron doesn't leak current)
4) Know what you're doing and make sure it's reversible.