Is the PRAM battery in need of replacement?

I have a MacBook 13 inch A1181 Core 2 Duo with 6Gb of RAM, and until recently it was doing very well. Super-fast boot-up and kept on for over 12 months at a time (with occasional restarts). Then, recently (about a month ago) I updated using Apple Software Update, and also Eye TV from 3.2 to 3.5 which was a vast mistake. After the computer almost stopped (locked up) upon the upgraded Eye TV launching for the "first" time, the "kernel task" shot up to nearly 90% of the processor. I threw Eye TV 3.5 into the trash and loaded Eye TV 3.3 which is somewhat better. Also, at the same time I foolishly upgraded Flash Player, which seems to have helped slow things down. Thinking I could handle this, I did not bother to check up what was happening and am now wondering how to fix this ever increasing problem.

After the upgrades, I noticed that when I put the computer to sleep (by closing the lid) it would not wake up. I had to do a "hard reset" every time. Then I when I connected my larger (40 inch) monitor to my computer, the screen would "re-gen" very slowly (remain blank for ages) then the screen on the computer would remain black while the larger monitor was OK. The computer could not recognise it's own "internal" monitor. I looked in the System Preferences and the monitor built-in to the computer did not even show up.

Then after I disconnected the external monitor, the only way to get the "internal" screen back was to do a hard reset.

Then the computer stopped "waking up" from sleep at all. Now, as a work-around, I turn the computer off every evening, starting-from-cold in the morning.

At nearly all times when running Eye TV, the Kernel Task was well over 90%. Also, when Safari was running a youtube video, the kernel task would shoot up to sometimes 108%.

I've reset the Parameter RAM (PRAM) three times and re-set the Power Management Unit servel times.

I think the Parameter RAM (PRAM) battery has died. I *think* this is the early 2009 model.

Is there any way to test the PRAM battery? If it is dead, how the heck can I replace it?

I tried burning a DVD for a friend of mine. It was a 3 Gb video file (of a TV program about light bulbs and planned obsolescence) going onto a 4.7 Gb DVD. The original file was an Eye TV recording. The encoding took 5 hours with the processors maxed out completely; the actual burn time was about 4 minutes, and the processors were barely noticing the load (ie: less than 5%)