Just do the math, its easy.
240 seconds * 96Khz (96,000) * 24 bits * 8 tracks = 4,423,680,000 bits
Divide it by 8 (8 bits =1 byte) and you get 552,960,000 bytes which is 552Mbytes
If you recorded at 24/48 it would be even less space.
Memory is important because once you use all your RAM, your computer will use your HD instead and RAM is much faster than a harddrive (RAM speed is in nanoseconds and HS speeds are in milliseconds).
P4's are good as well as Athlons, but you need to be more concerned with motherboard chipsets. There are significantly more compatability problems with motherboards for AMD processors that use the VIA chipset.
By using an Intel processor and motherboard/chipset, you can rest assured there will be no problems, especially with other DAW hardware. That has been my personal experience over the past 5-6 years.