I received a full set of upper dentures and a lower partial and I can not keep them in my mouth without gagging. I have tried to sleep with them so that I could get use to them but when I wake up I gag. Any suggestions this has caused great depression and I'm not sure how much longer I can feel this way

Sleeping with your dentures in is not recommended. Your tissues need a chance to breath.
Have you been back to where your dentures were made? They may be able to trim some of the plastic off the back of the denture. What you could do is wear them for a few hours a day and try to add a half hour longer each day.

I hope this helps a little.
Good luck.

Also try some Anbesol, Anbesol: Pfizer Consumer Healthcare (http://www.anbesol.com/index.asp) ,rub it on the back of the denture and put it in,the gag reflex is numbed for a while till you get acclimated to the new feeling.

And as flossie said, the back can be trimmed quite a bit,seek the dentist you had this done at,they know the symptoms.