64 bit operating system in a 32 bit structured computer

Almost 3 years ago I purchased a Dell 17R Inspiron Laptop from Dell  which I rarely use because it is soooo problematic.  Windows 7 with a 64 bit operating system.  Overheating  since the get go has ALWAYS been an issue - then powering off, but I digress.   

 I've spent countless hours with a Microsoft tech & have never been able to download Service Pack 1 for Windows 7 let alone IE 11.   When I boot in safe mode it shows hundreds of 32 bit drivers but NO 64 bit drivers. I finally asked a Microsoft tech that question & he told me to ask Dell, which is nearly impossible .  So I'm asking the community for answers .  Is it possible I have a 32 bit structured computer with a 64 bit operating system?  Thank you.