ok.
Now I really need to have a crystal clear understanding 1st.
You mention that you have 2 n810's?
I thought it was only one you were getting...
I didn't realize you purchased a pair of n810's...
If this is so...that was smart.
If my understanding is in error here please say so before I start going indepth into solutions that are not possible at this time for you.
In short..If you do have 2 n810's then yes you can pop in and use an os cloned sd card from another n810 ...
However it does not solve the problem of the issues of the n810 which needs reflashing, and proper setup.
And you would still need to install the proper boot loader to see the os on the sd card when it starts up.
You are starting to think outside the construct ...which is good.
here is a more concise (albeit short) thread on this particular topic.
http://talk.maemo.org/showthread.php?t=15374
Which will solve your problem.
There are other threads elsewhere here at talk maemo.
use the "Power Search" to the right ...in the column of on site links to find answers to questions.
Query "wording" is everything to finding the right answers for a specific solution for a specific problem.
And it is not as difficult as it sounds...although the process may appear daunting to a new person it isn't rocket science...and this little puzzle would speed up your learning curve and
You also have an edge with having the other n810.
Speaking of the problematic n810.
you mention it has wimax os on it?
Pop the back cover off
Pop the battery out
write down the info from the plate in there and compare/look-up what you see.
ie- n800= rx34 , n810=rx44, n810 wimax= rx48
It may be flashed with the wrong firmware...for the wrong device model.
the firmware in these lists....
https://web.archive.org/web/20131117...ev/nokia_N810/
for example... meant for a standard n810... will start with rx44 as can be seen.
which won't help for sure with issues.
Clearing that issue up may result in full functionality.
As far as application manager (from now on in conversation referred to as "app. man.") goes.
I'm betting the firmware isn't helping.
Also I'm betting the catalogues in the app. man. are nokia catalogues.
Which are gone.
They don't work.
Also I'm betting that even "maemo extras" catalogue isn't enabled.
Hence ...the most probable result is....
App. Man. "seems" broken.

1st thing.
Deal with the firmware issue...and flashing issue.
By the way...I know that you said the problem n810 won't connect via usb...
What have you tried?
Just plugging it in?
have you attempted to flash the firmware with the cable yet?
Give it a shot.
Make sure you know exactly which firmware you need 1st.
and have all pertinent stuffs ready as per flashing instructions found everywhere in the wiki, here at talk maemo, and my walkthroughs...first.

don't just hope to ride a half-solution like running an os on sd card... on top of another previous individ's created problems.
T
hat will lead to frustration and heartache.

After that flashing issue is properly dealt with ..all else is easy peasy