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I'm having all these same issues.  I've managed to uninstall all MS office 2013 and when I tried to reinstall it hung on step 1 for 10 hours (left it on while I went to work).  I've tried EVERY fix suggested but the one suggested here so will give that a go.

Dell sent me a new hard drive as I was still under warranty.  They believe something in the update corrupted the registry.  All is good now, but I no longer update automatically any Microsoft products.  Microsoft was so difficult to deal with.  I called them as it was an issue with a Microsoft product and they said it wasn't their concern as the Microsoft product was pre-installed by Dell.  Dell was phenomenal to deal with.  They tried everything they could to correct it, but just opted to get rid of the problem.

So it installed fine, now I'm getting the "There was a problem sending the command to the program" error again. Back to square one.

I haven't done any Windows updates after the install....

Run the Fix it:

http://support.microsoft.com/kb/2739501/en-us

this is the error code in cases where there is bad internet connection (when we say bad internet connection it does not mean the speed is not good)

You may check your internet connectivity by 

Windows key +X

Run CMD (as admin)

type: ping office.com -t

if it says request timed out, then better would be that you install the software on a different internet connection.

you may also try this commands to renew and flush the connection they may work, but will not solve the problem from the root.

Windows + x 

Run the Cmd  ( as admin)

ipconfig /release   -----once you run this command you will loose the internet connection

ipconfig /renew     ------the connection will be renewed

ipconfig /flushdns   ----- this command clears the cache

reboot your system, run the fix it and try to install the Office. if it does not work as advised before better would be switching the internet connection. 

I've been having all of the issues mentioned really, even down to having issues when uninstalling.

I emptied the Temp files as mentioned early on and ran the Microsoft uninstaller, and issues still occured.

Strangely this seemed to be my issue. I have a 100mb leased line....

I downloaded the ISO (2.1gb in less than 3 minutes, so my connection isn't bad!) from the Office website, burnt it to disc and installed it form disc. 

It's currently installing in the background, so looks promising

I actually had Microsoft do this for me via remote... It still isn't working... Can we get refunds and buy a diff version??? I needed to write a reference letter like 3 days ago and I cannot access Word