This has also happened to me. I was notified (in windows store) that there were updates to finance, sports, news, travel, Kindle. None of them will update and now I cannot install any new apps. It just says it could not install the update and uses error code: 80240437. As far as I can tell that is MS speak for "I don't know what happened!"
It has also happened this week to my daughters new dell tablet. I am running Windows 8 Pro and she is running Windows 8 RT. We have run the troubleshooter, the wsreset, checked the proxy, and are both using the MS virus checker. Based on the recent flurry of posts across the web I am beginning to think it is an update MS sent out. Short of completely stripping and reloading the machine, anyone have any more ideas?
I'm in exactly the same position.
I do have my wife's machine to compare mine with but currently she is working OK and getting updates without the uses error code: 80240437. I have done all the same diagnostics as you have but they haven't fixed it. I have also run DISM and SCF and they haven't found any errors.
I can't even find this error in the error logs with event viewer so can't really track down why it is happening.
It looks like it goes to the store correctly then starts to download and then comes up with the error. Is this what you are seeing?
Do you have any apps on the start screen with a "cross" on them? If you do then click on it and it should say something like "can't open app" and under this there is "go to store". Click on this and on mine it says "Your developer license has expired, please renew". If you get this it looks like the same issue.
Too me it looks like a corruption somewhere in this store that is impacting us or the store account has got corrupted either on our machines or in the store.