Superb Performance while on Battery???

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I have Medion Microstar notebook. It is P-IV 2.4GHz with 512 MB RAM and
40GB HD.

Since some months I am observing a very strange phenomenon:
1) After using my notebook for some hours on live power supply, it gets
quite hot.
2) The performance degrades considerably. Everything slows down. I can
feel it even while scrolling the web pages in Internet Explorer.
3) Now at this stage, if I pull-out the power supply and switch the
notebook to battery, everything is immediately turbo-charged and the
performance jumps to extreme in a fraction of millisecond. Everything
becomes so responsive and the notebook is sooooooo fast.
4) When upon the exhaustion of battery, I reconnect the supply, it
works good for some time, and then slowly starts becoming more and more

Could some of my learned fellows guide me on what could be the reason?

Sometime in the last year, my old power supply got burnt, and I bought
this new one (19V, 4.74A). Maybe this supply is a bit over-voltage?
Could it be the reason?

Furthermore, if I apply a slightly under-voltage supply (18V, for
example) for long time, would it damage my notebook?

Thanks for your replies.

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