I found this useful on the internet ..may be helpful to you- 
http://android-market-apk.en.softonic.com/android

Regards

Hardik Mangla

Chief Editor of TechiePlaza 

Thanks Hardik. I tried it and this apk seemed to install OK but the result's the same; updates are handled by the old Market software interface, and when you tap "update" it returns "download failed" And no, the disk isn't full! :)

Any other ideas?

Who's that then? Dell refused to help me, and I can't log any sort of a ticket with Google, I just get routed back to a FAQ on how to use the Store that doesn't work...!

You can show the device to the experts ..

Or you can update to Android 4.2.2

>>Posted by giveen replied on 07-25-2013 7:21 PM

Or you can update to Android 4.2.2<<

Sensible suggestion on the face of it... However, how would you suggest that I install an upgrade to the OS without the Play Store in a functional state? Where do I get hold of Android 4 to install?

Press vol down and power keys together to go to recovery mode then you can restore the updates and revert to factory conditions at ur own risk

I had a similar problem with the google store on my old tablet.  A few suggestions.  Go to your settings and tell the store app to return to factory default.  If that didn't fix it then go to anything in your settings that says google as the first word, such as play store and services; and I think there are maybe one or two more on android 4.0.  For each app click on it and hit clear data.  Restart the device.  That fixed my problem.  If I logged onto playstore from the desktop I found that google store was not seeing my device and identifying it at all...I think that was the issue after I went through the above it could finally see the device and identify it.  A few other suggestions I had found was to create another google account and switch to that then back to your own.  I don't think anyone really knows why this happens and it's happening to others but not a really common issue that you hear a lot about.