What is the difference between intel's p4 and dual core  

Pentium 4 brand refers to Intel's line of single-core mainstream desktop and laptop central processing units (CPUs).
Dual Core refers to a new Central Processing Unit (CPU) has two processor cores on one die essentially like having a dual processor system in one processor.
The difference between a single core and a dual core is that a dual core system has two CPU’s that are electronically wired together.
Quad Core is a type of multi-core technology that includes two separate dual-core dies, where dial-core means a CPU that includes two complete execution cores per physical processor installed together in one CPU package. In this set-up cores 1 and 2 would share a memory cache, as would cores 3 and 4.

Dual core is quite handy to have when it comes to gaming and vista. Between that, a couple of gigs of ram (vista needs 3 to run smoothly) and a decent video card, you cold probably run some of the higher end games on medium to high settings with little lag. But too it depends on what type of 3d games you play. If it's Crysis then the only way to run on high settings is to completely max out your computer. But if it's something like Dark Age of Camelot, then dual core, two gigs of ram, and 8600GT video card will do you just fine (that's what I have)

beh normally the good skill to have wo or more core in your processor is that the system must be better and have a better capability to elabarate dates together!!Your processor is a single core..so it does not mena that it don't work but have teorically a few base of elabarate dates than in multiple core!!
I think if you have vista and like games,normally they are application so heavy and needs so much controls more..so having a processor with two or more core will be suitable and your experience much be better!!
In fact now the last laptop/desktop with vista are based on the intel core duo 2 such multiple core to elborate better graphics,dates,upload,download,and even the complex controls inside vista!!