You don't need a modded PS2 to boot PRESSED HDLoader discs. BURNED discs are another story. You need to mod your system to boot burned discs.
If you buy a HDLoader disc, it's probably pressed, so it has the data that your burner can't write to the disc on it.
My PlayStation2 HDD guide.
NTSC J SCPH 30000 with HDD and PSBBN 0.32
NTSC U/C SCPH 30001R Astral Blue LE PS2
Final Fantasy XI status:
Server - Ragnarok, Race - Mithra, Jobs - BLM 72 WHM 51 SCH 39 SMN 25, Nationality - Windurst, Name - Bungiefan