Or look around for a 2nd hnd comp around 2.0ghz or so & upgrade with whatever parts you want, for better performance you want a CPU that's an AMD Athlon steering clear of the AMD sempron & for Intel you want Pentium steering clear of celeron

AGP is long dead, it was replaced by PCI Express more than 6 years ago.
Anything sold as AGP in 2006 onwards was not designed as an AGP card, rather just also available as an AGP model for people who hadn't upgraded their PCs to PCI Express yet.
This is one of the reasons I used to go around telling people not to buy hugely expensive AGP cards for their systems as they weren't worth it when the rest of the system needed upgrading. With the exception of some dodgy hybrid boards you haven't been able to buy AGP systems since the early P4 days.

When you say your AGP cards are 'fairly decent', what actually are they? Most AGP cards are a lot weaker than you may think.

Whether building a new system is cheaper than buying one pre-built really depends on cost. If you're building a low-end system for a very minimal price then yes, it's cheaper to buy one pre-built as not only do manufacturers get huge deals on the cheapest hardware, but they also use lower-end hardware than you can actually buy as individual components. Plus, they can throw in an operating system for free, which you will have to pay end-user money for, i.e. a lot [if you want a legitimate copy of course]

As the budget rises, so do the markups that prebuilt system manufacturers make. They fleece you like hell for upgraded components to add extra performance to the system and very quickly it becomes cheaper to pre-build, but a crossover point does nonetheless exist, so if you're only looking to spend something like £200/$300 on a new system and need to replace all of the parts [that sounds like a given since your cards are AGP] then a prebuild may be for you.
If you're upgrading to play games however, a budget basic PC isn't going to cut it and you're going to want to spend at least £350/$450 for a system that has basic gaming potential, preferably more.

Here's how the 7600GT stacks up against current low-budget and midrange cards, in terms of relative performance.

7600GT: 100%

8500GT: 40%
8600GT: 125%
8600GTS: 155%

9400GT: 45%
9500GT: 155%

G210: 30%
GT220: 210%
GT240: 420%
GTS250: 625%

GT430: 260-360%
GTS450: 830%
GTX460: 1100%
GTX465: 1160%
GTX460 1GB: 1200%

AMD Integrated graphics (790/890GX): 60%
Intel Integrated graphics (Core 2 G45): 25%
Intel Integrated graphics (Pentium G6950): 35%
Intel Integrated graphics (Core i3/i5): 50%
Intel Integrated graphics (Core i5 661): 60%
Intel Integrated graphics (Core i5 2000): 110%

HD2400 Pro: 25%
HD2600 Pro: 45%
HD2400 XT: 50%
HD2600 XT: 85%

HD3450: 25%
HD3470: 75%
HD3650: 135%
HD3690: 185%

HD4350: 35%
HD4450: 75%
HD4470: 80%
HD4550: 105%
HD4650: 225%
HD4670: 390%

HD5450: 100%
HD5570: 420%
HD5670: 490%
HD5750: 660%
HD5770: 770%

HD6850: 1300%
HD6870: 1470%





As you can see, it's still more powerful than older budget cards, but current inexpensives like the $40 HD5450 are equals to it, and as soon as you spend more, it's left in the dust.
The HD5670 is $80, yet it's five times as powerful.
Reach the sort of prices you may have paid for the 7600GT in its heyday, and it's night and day. The $160 GTX460 is 11 times as powerful, and the $180 HD6850 is 13 times as powerful.
You may also notice that the integrated graphics that come built into new Intel Sandy bridge CPUs are actually faster than the 7600GT as well. Food for thought indeed.

With building a new system, not a lot has changed to be honest. Different technologies have come along, so what's compatible with what will have changed, but the fundamental principle is exactly the same.