I suspect you need a repaste , my G5-s use to crash or hang during working (true after loading OS X) because of overheat . (main issue is that's a big job to do).
Better try external DVD-RW , should boot from it , or build a usb thumb drive formated + restored from tiger/leopard .dmg(img/iso).
Mount your hdd drive on a windows pc , delete everything(partitions) from Disk Management , create 1 partition , do a chkdsk , then delete the big partion , turn off pc or eject the mac G5 drive , and reinstall it into the MAC G5 , if disc (cd) appears at option key , load the disc , then try moving with the install , it should let you initialize/format in PowerMac mode.
As for the second one , elaborate? 2 beeps? rams?try 2x Identical dims ... clean dimm with eraser or/and contact cleaner +tooth brush , you can use same contact cleaner on slots.
(I am testing G5 for endurance , runing same system since 2008 so 15 years a 20 year old system) they are not building stuff like this anymore.... (sometimes it refuses to powerup , so I smake-it till it cycles-up from powerbuton).
It's still running solid. (yesterday updated a few things software wise-like the elcapitan theme-and some scripts , but turned out it just slowed things down, got lower score than before).