A dual core processor along with 4G of RAM should be plenty of processing power and processing real estate. There is definitely some process going on if the problem is "predictable" within a short time after boot.
Let's search for more clues. First, if indexing is turned on, turn it off. Then, click "Start", "All Programs", "Accessories", "System Tools", and "Resource Monitor". Watch especially the graphs and percentages for CPU and memory. They should reflect your problem and help track down the offending process(es).
Other things that might affect your problem are disk (partition) size and percentage full, fragmentation of files, and things such as that. Let us know what you find. There may be others with the same problem...