I have heard before "I don't need more than 1GB or 2GB." And I know how OS X and Safari and every app works with low memory or with adequate and yours is on the anemic starvation under nurished side. 512MB DIMMs are also a problem.
RAM can do funny things. And with a 7 yr old system, and seems you were not cleaning out the dust and pulling the X1900 enough, like 3-4x a year, it has more chances of "old age" compared to if it was maintained.
FBDIMMs use to run too hot, needed extra cooling, and dust blocks them from releasing heat. When a system goes to sleep the heat inside actually builds, it does not cool down. Which is why when you restart it should and will run the fans at high speed at first on start or wake from sleep.
I can upgrade and get Mac running fast and smooth, but not in the configuration it is in.
But there is no majic answer I have other than treat everything as possible cause and start from scratch on everything. SMC Reset. Maybe new PRAM battery - I never do. Inspect parts and how they look.
My Mac Pro 1,1 runs better today with upgrades and such and clean install of Lion (I do recommend going to 10.7.5) along with RAM (I needed more than 8GB when I started using iPhoto a lot along with everything else). The SSD made it FAST - 10 seconds after login for 12 programs to be open and ready to use, 10 seconds to boot (rare ever do).
With any system bought used of course I would be careful, they may not have understood what to do and how to do it. But first thing to do is install a new hard drive and fresh OS.
Couple things to monitor temps, get dust out, etc and kick it into high gear. SSD is good no matter what and for this or another system (need Icy Dock adapter to install into one of the drive bays $15) But CLEAN out dust everywhere, with care, CLEAN OS and keep the FBDIMMs below 70*C you may need to boost the fans to 900 rpm - until you replace the X1900 and get at least one set of the Amazon linked RAM.
SSD: Samsung 840 128GB
http://www.amazon.com/Samsung-Series-120GB-internal-MZ-7TD120BW/dp/B009NHAF06/
WD Black 1TB $85
http://www.amazon.com/Western-Digital-Caviar-Internal-Desktop/dp/B0036Q7MV0/
WD Green 3TB $149 - (might want WD RED NAS/RAID 3TB though)
http://www.amazon.com/Western-Digital-Caviar-Green-Desktop/dp/B004RORMF6/
Sonnet Technologies Tempo SSD 6Gb/s SATA PCIe
http://eshop.macsales.com/item/Sonnet%20Technologies/TSATA6SSDE/
Resetting the System Management Controller (SMC)
https://support.apple.com/kb/HT3964
General Help
http://pondini.org
Final Cut Pro X, Motion 5, Compressor 4: Graphics card compatibility
http://support.apple.com/kb/HT4664
http://www.apple.com/finalcutpro/specs/
Temperature Monitor
https://www.macupdate.com/app/mac/12381/temperature-monitor
http://www.bresink.com/osx/HardwareMonitor.html
SMCFanControl 2.4+
https://www.macupdate.com/app/mac/23049/smcfancontrol
UPS
http://www.amazon.com/CyberPower-CP1500PFCLCD-Compatible-1500VA-Tower/dp/B00429N 19W/
Metro Vacuum ED500 DataVac 500-Watt 0.75-HP Electric Duster 120-Volt
www.amazon.com/Metro-Vacuum-ED500-500-Watt-Electric/dp/B001J4ZOAW/