Welcome to the PlaneShift forums...
I use an Intel laptop with Windows 7 OS.
"Laptop" already sounds bad; they often don't have specific "gaming hardware".
I'm not sure how to get the stats for it
How many of the previous topics about crashes did you
not read? Certainly those recommending e.g.
HWiNFO as free and powerful system analysis tool (use the green "↓ DOWNLOAD INSTALLER" buttons near the bottom and select e.g. the "Local (U.S.)" link for the
Windows 32-bit version).
The most interesting part of information about your PC is certainly your graphic chipset. You should use the most recent drivers provided by its manufacturer; never rely on graphic drivers installed via the Windows Update, they often lack in support for the OpenGL graphics interface which multi-platform games like PlaneShift prefer over the Windows-only Direct3D interface.
I can't get the game to even update on my desktop because it says something about not having the permission to do so.
Use the Windows Explorer; navigate to the directory where PlaneShift was installed into (e.g. C:\Program Files\PlaneShift); right-click the pslaunch.exe; select "Run as Administrator".
This was documented in dozens of threads before...