The Browser screen appears if it fails to see a boot disk. From what you describe, it does eventually see the boot disk. You might want to open the PS2 and look at the chip installation to see if, say, PIN #4 is intermittent. This is not really in my bailiwick but if it's not your CDs then it has to be something else associated with the boot process; a modchip perhaps.

Woodmaster101 posted these oinouts for NEO2.2:
PIN #1 = supplies + (power) to the chip
PIN #2 = sends SCE signal out to PS 2
PIN #3 = PS 2 drive tray pulse tells the BA5810FP chip whether to expect a drive tray open or close
PIN #4 = checks/signals RESET button on the PS 2
PIN #5 = closes PS 2 drive tray
PIN #6 = opens PS 2 drive tray
PIN #7 = checks if game CD is PSX/PS 2 (If PS 2, immediately stops SCE signal & restarts when a "tray close" is seen. If PSX, it stops after about 15-20 seconds)
PIN #8 = supplies ground to the chip