From what I can find, your laptop has "Intel HD Graphics", which should fully support hardware rendering up to DirectX 10. (Source:
http://en.wikipedia.org/wiki/Comparison_of_Intel_graphics_processing_units)
Meaning your current computer should work fine.
1. Definitely check for new video drivers from HP first. If not from HP then from
Intel's download page2. Your Power profile in Windows could prevent hardware acceleration. Make sure the "High Performance" power profile is selected.
3. There's an "Intel(R) GMA Driver for Mobile" Control Panel in Windows on my netbook, I imagine you have something very similar. This Control Panel has power savings options that could potentially be causing a problem.
It's also possible there's a bug with Inner Space that currently only happens with Intel graphics + Flash, but that I can't currently reproduce... I may need to pick up new hardware to reproduce the problem.