Random shut down issue

Question

So I have a Macbook 13" 1.83 Ghz Core Duo, running 10.6.2 with 2gb of (user installed) RAM. Minus a defective battery issue last year (the battery swelled to the point where my trackpad wouldn't work) which apple replaced for free out of warrantee, I have had no issues.
Out of the blue, I've been experiencing random shut down issues of sorts. If I have the computer plugged in it works fine. Sometimes though, the computer will randomly shut down after being unplugged. I tried reseting the SMU but it didn't seem to do anything.
Another odd thing - I calibrated the battery with the computer on an incline on my desk to keep it cool in case it was an issue of over heating. The computer charged fully, and then drained it's charge to 0% and went to sleep as it should.
But once I charged it up about halfway again, unplugged it, and put it on my lap, it shut off within 2 minutes. I'm well out of my warrantee so any user suggested diagnostic tips would be appreciated! I've included the battery info for good measure (btw the battery is not even a year old).
Battery/power info:
Model Information:
Manufacturer: DP
Device name: ASMB016
Pack Lot Code: 0002
PCB Lot Code: 0000
Firmware Version: 0110
Hardware Revision: 0500
Cell Revision: 0200
Charge Information:
Charge remaining (mAh): 3610
Fully charged: No
Charging: Yes
Full charge capacity (mAh): 4310
Health Information:
Cycle count: 247
Condition: Normal
Battery Installed: Yes
Amperage (mA): 783
Voltage (mV): 12406
System Power Settings:
AC Power:
System Sleep Timer (Minutes): 4
Disk Sleep Timer (Minutes): 10
Display Sleep Timer (Minutes): 4
Automatic Restart On Power Loss: No
Wake On AC Change: No
Wake On Clamshell Open: Yes
Wake On LAN: No
Current Power Source: Yes
Display Sleep Uses Dim: No
Battery Power:
System Sleep Timer (Minutes): 6
Disk Sleep Timer (Minutes): 10
Display Sleep Timer (Minutes): 5
Wake On AC Change: No
Wake On Clamshell Open: Yes
Display Sleep Uses Dim: No
Reduce Brightness: Yes
Hardware Configuration:
UPS Installed: No
AC Charger Information:
Connected: Yes
ID: 0x0100
Wattage (W): 60
Revision: 0x0000
Family: 0x00ba
Serial Number: 0x002afaac
Charging: Yes

Answer 1

Hmm, your battery is fairly healthy.
Is your fan running?
You can get the iStat Pro widget here:
http://www.apple.com/downloads/dashboard/status/istatpro.html
The iStat widget measures various parts of your computer, including the fan speed.
~Lyssa