Especially these days, if a system is old, then it may be even more difficult to find the parts, and building a low-budget system is not too difficult, and there isn't too much of financial pressure either.
I'm thinking of having 4 posts, of building your own PC, ranging from extreme low budget to extreme high budget. The first shot - low budget PC. Keep in mind that these posts are solely based on my thoughts, and you may disagree, but the amount of budget may be different to everyone.
Low Budget PC -
CPU
AMD Athlon II X2 Regor 3.4 GHz Dual-CoreSocket AM3
TD Power 65W
Hyper Transport 4000 MHz
2 x 1MB L2 Cache
45nm Manufacturing
$55
AMD Athlon II X3 Rana 3.2 GHz Triple-Core
Socket AM3
TD Power 95W
Hyper Transport 4000 MHz
3 x 128 KB L1 Cache, 3 x 512KB L2 Cache
45 nm Manufacturing
$70
Motherboard
BIOSTAR 760G Micro ATX - A780L3BAMD 760G / AMD SB700 (North / South Bridge)
2 x 240 pin memory slot, supporting DDR 3 800/1066/1333 / up to 16GB / Dual Channel
1 PCI Express 2.0 x16
1 PCI Slot
4 SATA 3Gb/s
ATI Radeon 3000 on board video
$45
RAM
CORSAIR XMS3 4 GB (2 x 2GB) DDR 3 1333 Dual Channelcas Latency 9
Timing 9-9-9-24
1.6V
$25 - $30
VGA
Radeon HD 5550 1GB PCI Express 2.0 x16550 MHz Core Clock, 800 MHz Memory Clock
$50 - $55
Case
Diablotek RPA-0710 ATX Mid Tower400W Power Supply included
$25
HDD
Seagate Barracuda 1TB7200 RPM
64MB Cache
SATA 6.0 Gb/s
Average latency 4.16 ms
$80
Other peripherals, such as monitors, keyboard and mouse, are little too difficult to jot down here. Low budget PCs are typically for web browsing, storing data and a few document work to do, so I'd say go with the cheapest keyboards and mice possible. Monitors are also one of the important part of a computing system, especially it will affect your eyes directly, so I'd say you should look at more decent ones, instead of going with a cheaper one, for your eye comfort.
Without any other parts, above will end up with about $300 in total. This is actually lower than the 'low budget' I had in mind, so let's see how the "extreme low budget" system comes out!
Happy computing!