13"Macbook shuts down unexpectedly 10.5.8

Question

I have a MacBook 13" (2008 I think) running 10.5.8.
In January I had to have a new logic board after it failed to switch on after a period of running very slow and freezing.
All ok for some time, but then I started to get unexpected shut downs/restarts. Both with and without power supply connected. Also had the first 2 instances of the emergency shut down window and kernal panic notification. Every couple of days it just restarts all on its own. I think is when I am seeing a video or have several applications open at once, but not sure.
I have run diagnostics and first aid and verifications etc and all comes back ok.
My partner uses PC and says a PC behaves like this when it overheats. Is that possible for this Mac?
Is this a hardware problem?
Thanks.
Fi
Utilities say:
Power On Self-Test:
  Last Run:          12/06/2011 09:23
  Result:          Passed
Battery Information:
  Model Information:
  Serial Number:          DP-ASMB016-374f-2d5
  Manufacturer:          DP
  Device name:          ASMB016
  Pack Lot Code:          0002
  PCB Lot Code:          0000
  Firmware Version:          102a
  Hardware Revision:          0500
  Cell Revision:          0102
  Charge Information:
  Charge remaining (mAh):          2108
  Fully charged:          No
  Charging:          Yes
  Full charge capacity (mAh):          4903
  Health Information:
  Cycle count:          808
  Condition:          Good
  Battery Installed:          Yes
  Amperage (mA):          2099
  Voltage (mV):          11658
System Power Settings:
  AC Power:
  System Sleep Timer (Minutes):          90
  Disk Sleep Timer (Minutes):          10
  Display Sleep Timer (Minutes):          90
  Automatic Restart On Power Loss:          No
  Wake On AC Change:          No
  Wake On Clamshell Open:          Yes
  Wake On LAN:          Yes
  Display Sleep Uses Dim:          Yes
  Battery Power:
  System Sleep Timer (Minutes):          10
  Disk Sleep Timer (Minutes):          10
  Display Sleep Timer (Minutes):          2
  Wake On AC Change:          No
  Wake On Clamshell Open:          Yes
  Display Sleep Uses Dim:          Yes
  Reduce Brightness:          Yes

Answer 1

The usual steps for resolving this type of issue are
- Reset the PRAM: http://support.apple.com/kb/HT1379
- Reset the SMC: http://support.apple.com/kb/HT3964
- Maybe calibrate the battery? http://support.apple.com/kb/HT1490
I would also download Onyx and work through its set of verification, maintenance and cache cleaning procedures, by going left to right through its tool bar.  If you're still having problems after all these steps then it's time to visit the Apple Genius!
Bob