How to Install Ubantu 9.04 64 bit in Vista32 bit, having Pentium Dual Core & 512 Nvidia graphic Card?

You "tried" to install it? Or it WAS "installed inside windows"?
You installed it "inside Windows" using WUBI?
It gives up...what gives up? When do you get the error? Immediately after clicking the launcher or after it starts running for a while and tries to load the desktop?

Please provide more detail for people to help you.

Also, you might want to check if it is even possible to run 64-bit Ubuntu in a 32-bit OS environment - my inclination is that you cannot. It would be kind of like trying to run a 64-bit virtual machine on a 32-bit host...just can't happen.

I'd try downloading the 32-bit Ubuntu version and use that.

Also, try booting from the CD and selecting the option to try Ubuntu without modifying your system. This will run the so-called Live CD and give you a preview of Ubuntu. If you like it, then you can decide later to install it in Windows with WUBI, or install it directly to the hard drive. However, 64-bit Ubuntu Live CD will not run on your system if it's not a 64-bit CPU. To find out if your CPU supports 64-bit, visit http://www.grc.com/securable.htm and download it. Run it and the maximum bit length is what your looking for. If it's 32, then you have a 32-bit CPU. If it's 64, then you have a 64-bit CPU.

Ok try booting up from the cd and hopefully you should get to a menyu with "Try Ubuntu without chagnes to the machine" choosing this option should get you to a working desktop which should give a fair idea of how Ubuntu will look on your machine. This working desktop is called a "LiveCd sesion", if it works and most version of linux have it as their default option when booting up their installer cd. here's a guide if you have trouble getting to that first menu
https://help.ubuntu.com/community/BootFromCD
it might be worth checking the cd is alright, this guide might help
https://help.ubuntu.com/community/BurningIsoHowto

If the LiveCd session work then you should be able to surf the internet into here directly from firefox on the top taskbar, it should pick-up on your internet connection :) Then just use the icon in the top left-hand corner to install Ubuntu in the proper dual-boot way so that you can keep popping back into Windows at least until you've got used to doing everything in linux. Most of us keep a dual-boot like this anyway
https://help.ubuntu.com/community/WindowsDualBoot

Good luck and regards from
Tom :)