Hi laura-in-hawaii
I apologise that you haven't had a response to this question previously and understand you may never read this post. However, I will endeavour to answer your question.
This problem sounds very much related to a overheating issue. The
CPU of the laptop is normally located at the top (where the keyboard ends and the monitor begins). This would mean that as the
cpu warms up, the monitor is being effected quite harshley...unfortunately there isn't alot you will be able to do about it without voiding any sort of warranty/further damaging the laptop.
I'd suggest taking it to a local HP authorised repair centre and getting them to look at it for you.
Marked as Answered - if you have any queries please ask them and i will answer them for you. If you read this post.