There are various ways to make the console perform the double-boot process. A bad flash in the modchip/TSOP can do it (eg, using a BIOS intended for a different console version), as can
most problems related to the motherboard.
If the LED is lit green, the DVD drive is unresponsive, and the console is giving no video/audio output, then the console is indeed having trouble reading from the TSOP. This set of symptoms is usually referred to as a "coma console".
If the TSOP has been flashed with FlashBIOS, then as mentioned, there may not be much point to getting the console to boot off it.
FlashBIOS is a legal BIOS distributed with modchips. When the user gets the chip, they boot the console, FlashBIOS loads, and they can then reflash the chip with a "normal" BIOS of their choice. However, FlashBIOS doesn't know how to flash a TSOP - so if you flash FlashBIOS into a TSOP, then whenever the console boots off that chip, it'll only ever load FlashBIOS (which won't be able to replace itself with anything else). In short, you'd need to install a modchip in order to get the console to boot a different BIOS.
However! It just so happens that the
traditional fix for coma consoles might also provide a workaround for this. If you are able to get the console to boot one of the secondary stock BIOS copies stored in the TSOP, then you should be able to install a softmod and reflash the TSOP with something more practical.
On the other hand, it's quite possible that when you flashed FlashBIOS to the TSOP, you removed all the "backup" copies of the stock BIOS. Meaning that you'll HAVE to use a modchip with this system from now on, full stop.
Only way to find out for sure is to try it and see...
Edit: Well, that said, there ARE ways to reflash a TSOP while using a modchip, but you'll need certain TYPES of modchips. Refer to the site
tutorials section for more information on these.