Ubuntu – 8 GB RAM on 64 bit processor using 32 bit Ubuntu

This is due to the Mobile Intel 945GM Express in your laptop.

I own a Thinkpad T60, which uses the same chipset. It was one of the first northbridges from intel for the Core2Duo 64-bit CPUs. They failed in designing it.

The chipset can only theoretically address 4GB of RAM, yet also has to address other hardware (I/O memory). It reserves the upper 1GB memory range for that. The 64bit logical memory address support in the Linux kernel doesn't help, because the mainboard and northbridge only provide for a 32bit physical address bus to the CPU. And there is no workaround.
http://forums.lenovo.com/t5/T61-and-prior-T-series-ThinkPad/Thinkpad-s-and-N100-s-w-945PM-chipset-can-t-address-gt-3G-Ram/m-p/2730

There is a theoretical option in devising memory bank switching. Yet the kernel does not support it, nor would it make sense on the x86 architecture. The i810 memory controller of the 945GM is probably too lazy for that to make sense.

You should install 64-bit. You have a modern 64-bit processor and plenty of RAM. It's no longer the case that the 64-bit version is less stable, and virtually all software is available for both platforms.

I would say the only reason you should consider installing the 32-bit version is if there's some key piece of software that you need which is only available as a 32-bit version.