Hello, community. I posted this in another thread, but I now believe it's a separate issue, so I'm floating it separately to see if anyone has any ideas:

My entire system will freeze seemingly at random: sometimes when it's doing something (e.g. compiling, installing things), sometimes when it's just sitting around and I haven't touched it for several minutes - in any case it happens even with suspend and brightness reduction turned off. This has happened with a wide variety of applications open, and it does not seem to have anything to do with any individual programs. The system does not respond to SysRQ commands when it has locked up in this way. The machine is an essentially brand new HP Pavilion dm1-4010us, and it has done this in both a 64-bit installation upgraded from 11.10 and a 32-bit fresh installation of 12.04. I have it dual-booting Windows 7, and have not encountered any issues on Windows.

System specs are:
AMD E-450 Processor
4GB RAM, memtested and it's fine
Radeon HD 6320 Graphics
Broadcom BCM4313 Wireless controller, which has given me trouble before on 11.10

Though I am by no means an expert, I suspect the wireless controller may be related somehow: on 11.10, before I used the driver workaround in the networking support forum, I was getting much more frequent lockups along with unacceptably terrible wi-fi performance. The SysRQ keys DID work for these lockups. Once I did the driver override, wi-fi performance dramatically improved but I continued experiencing these freezes, and SysRQ no longer worked during them. I notice that the wi-fi fix appears to be applied by default in 12.04, as I did not have to do anything to get acceptable performance out of it when I reinstalled.

Two additional points:
-When this happens with audio playing, it stops immediately.
-This has occurred both with open-source video drivers and with flgrx (post-release updates) in use.

Anyone who has any theories or ideas for additional tests to perform, let me know and I'll try them as I'm able. I use Ubuntu for work and this is really making it hard to get anything done.