I'm using an old Gateway to dual boot between FreeBSD and Debian. I had trouble compiling a kernel on FreeBSD so I used my other FreeBSD box to compile the kernel, then transferred the kernel to the problematic FreeBSD box. It works fine.

Next thing I wanted to do is set up a VPN using Linux. I configured a kernel and tried to compile it but the computer freezes the same way it did w/ FreeBSD. I poked around in CMOS but didn't see anything that would affect this.

Two questions:
1) is there any reason that anyone knows of why this desktop freezes?

2) Can I cross compile the Linux kernel on FreeBSD and move the kernel image over to the problematic desktop?

Thanks in advance

Most times computer freezes/crashes during kernel build are caused by overheating problems, especially if it freezes/crashes a little while after starting the build.

If it's an old computer, make sure the cooling vents are clear and that the CPU heasink is cleaned and the fans are all working properly.

You may also throttle the CPU speed back during the build if FreeBSD allows that. Also try the -j1 make option to limit the number of concurrent make jobs.

Try memtest for a few days.

As above heat.

Also set bios to slowest settings like failsafe or default.

From my experience: Freezes are almost always related to a bad PSU or faulty voltage regulators on the board. Overheating may be an issue, but on modern processors there are security options enabled. At first they will reduce clockspeed and voltage when overheating, if that isn't enough they shut down the system. Normally they don't freeze. Cleaning the cooling system is always a good idea, of course, try it and have a look at the temperatures when compiling the kernel.
If overheating isn't the problem try it with a different PSU and look for bend capacitors on the board.