How can I fix my hp laptop?

I have an HP laptop that has a few quirks...

Sometimes when I try to dial up, I get a high pitched tone instead of a dial tone and when the modem attempts to dial, I get squeaks instead of number tones...

I recently upgraded my Quicken program and ever since, I cannot shut the computer down. It goes thru all the cycles until it reaches a striped screen and then it freezes. I have to hold the power up button for five seconds in order for the computer to shut down.

Occasionally, the 'backspace', 'g', 'h' and 'escape' keys will stop working. After a while, they'll come back.

Does anyone have similar types of headaches and are there any suggestions on what to do to fix? I've brought it to a repair shop but they could not duplicate the problems.

Thanks,