Homebrew on umodified slimlines.
Yes, it can be done without messing with your lid sensor.
You need an elf loader that is on a working ps2 CD.
The AR MAX contains an elf loader. It does not work very well, but it will load some software. Getting a launcher binary that is compatible with said loader is the best way to get homebrew running without buying hong kong products. To use the elf loader, simply put your elf on a USB drive or UMCDR CD, and enter max media player. We here at ps2-scene don't condone UMCDR, so instead use your USB pen drive. I suggest your launcher binary be launch elf, as it has USB support as well, if you cna figure out how to make a version that boots.
Other discs that contain elf loaders include Swap Magic (latest version) and pro-loader. These are both hong kong products desined for piracy, but at least swap magic isn't ripping off other software. TO use their loader, you must place your elf in a save with the correct name for the save AND the elf, and use a cheat device to transfer the save over USB to your memcard. If you refuse to buy an AR MAX (and i can't blame you for this!) you must buy swap magic or pro loader, and use codebreaker to transfer the save. The user guide for swap magic and pro loader will tell you the names.
Unfortunately i know of no other products with ELF loaders. It is my wish that someone make a ps2 cd that has an elf loader on it that supports USB and hard drive.