G5 iMac/Finder Freezing

Question

This happens most often in the morning when I leave the machine on overnight to use some non peek bandwith.
When I go to check the computer in the morning it shows the time as being some point in the middle of the night. I try and start an application the beach ball starts spinning. It requires a hard start to get going again.
I have tried changing sleep settings to only sleep the hard drive and screen and unplugged all USB devices apart from the mouse overnight.
Unfortunately the problem still persists.
Here how this were set when I went to bed last night:
I had transmission running, set to begin torrents (4) during my off peak period (2am-10am). No other applications were running.
When I woke up this morning I hit the space bar to wake the screen (at about 6.40am) the time on the screen was 12.11pm. Because it had frozen before 2am no torrents had begun. As soon as I tried to use transmission or use Force Quit to restart the beachball appears and nothing is responsive.
I am forced to do a hard restart.

Answer 1

It not a laptop so no battery, sorry to be an uber noob but what effect does resetting the PRAM have on the computer, are setting lost? Thanks for your help Miriam.
Also:
Here's the console info from the night before last, you can see the restart at around the 7.06am mark, last log before that was 1.25:03am which is about the time displayed in finder when i woke the screen:
Jul 8 00:00:12 Macintosh newsyslog[6131]: logfile turned over
Jul 8 00:25:03 Macintosh kernel[0]: SetCryptoKey R: len 32, idx 1
Jul 8 01:25:03 Macintosh kernel[0]: SetCryptoKey R: len 32, idx 2
Jul 8 07:06:08 localhost kernel[0]: Darwin Kernel Version 9.4.0: Mon Jun 9 19:36:17 PDT 2008; root:xnu-1228.5.20~1/RELEASE_PPC
Jul 8 07:06:01 localhost com.apple.launchctl.System[2]:
kern.ipc.maxsockbuf: 8388608 -> 512000
Jul 8 07:06:01 localhost com.apple.launchctl.System[2]:
net.inet.tcp.sendspace: 65536 -> 131072
Jul 8 07:06:01 localhost com.apple.launchctl.System[2]:
net.inet.tcp.recvspace: 65536 -> 358400
Jul 8 07:06:01 localhost com.apple.launchctl.System[2]: fsck_hfs:
Volume is journaled. No checking performed.