Can you see the output of the boot process, or do all distibutions you have installed use a bootsplash to hide this information? Ich you are able to enter the boot manager (I'm assuming its's grub here) you may want to edit the boot entries and remove any "silent" or "quiet" flags.
If your machine prints "loading grub" or something similar try pressing ESC a few times to enter the boot loader's menu. Sometimes this isn't even required, since the boot loader always displays this menu. 
Then you should be able to select a boot entry with the cursor keys. (Press ANY key to prevent your machine to continue booting due to a timeout)
Mark the preselected entry and press e. You'll be able to edit the entry just like a textfile. Remove the flags and follow the instructions on screen to boot. On Debian hit Ctrl+x to boot.
(note the flag quiet on line 6 - which is line 8 actually)
