Dell Studio 1435 CPU upgrade

Yes you can, here are the specs. Intel® Core™2 Duo Processor T6500 (2M Cache, 2.10 GHz, 800 MHz FSB) Socket 478 [PPGA478] 

http://dell4laptops.blogspot.com/2009/10/dell-studio-1435-laptop-product.html

your CPU can utalize a 64-bit Operating System

Intel® 64 architecture delivers 64-bit computing on server, workstation, desktop and mobile platforms when combined with supporting software.¹ Intel 64 architecture improves performance by allowing systems to address more than 4 GB of both virtual and physical memory.

You may find that it runs better in 64-bit mode with more RAM.

But if you insist on upgrading try this: Intel® Core™2 Duo Processor T7800 (4M Cache, 2.60 GHz, 800 MHz FSB)

http://ark.intel.com/products/31729/Intel-Core2-Duo-Processor-T7800-4M-Cache-2_60-GHz-800-MHz-FSB