Macbook only shuts down when battery is flat and date and time revert to 2008

Question

Hey Guys
My Macbook only shuts down when the battery goes flat.
When I switch it back on everything seems to be fine though the date and time are incorrect. Seems to go to default date which is 2008.
Other things seem to affect my browser, Facebook won't login properly and certain websites seem to propmt that the website can't be trusted, which is strange because gmail is one of them and should be fine.
Appreciate all the help from you cyber friendly folks!
My system specs
2.2 Ghz
4GB
MAC OS X Version 10.6.8

Answer 1

To answer your questions in sequence:
1) You can't, really: the symptoms your Mac is exhibiting point at a loose or next-to-dead back-up battery. Only way to find out is to test it, and to do that, you must open your machine, locate the battery and test it with a battery tester (see here for more info on how to open your Mac; make sure to select the right model)
2) It's actually the opposite: when you must use your Mac on the battery, well, then, do it, but if you're sitting at your desk, or, like me, on your sofa, with your MBP on your lap, simply keep it plugged into the main.
An additional measure to preserve your battery, that applies less to the recent Unibody design, but is helpful for ealier adopters of the MacBook Pro: don't leave your machine plugged in when it's turned off; it prevents a slow, natural depletion of the battery, and will play against you in the long run.
Last but not least: battery calibration is required once a month for older MacBook Pro models (non-Unibody, basically). If your machine belongs to that era kids the age of Justin B. don't even imagine ever existed, check here.