You system's first boot on its own power is what electrical engineers call the „smoke test“.
If you are booting directly into Debian, and the system doesn't start up, either use your original installation boot media (for instance, the rescue floppy), or insert the custom boot floppy if you created one, and reset your system. If you are not using the custom boot floppy, you will probably need to add some boot arguments. If booting with the rescue floppy or similar technique, you need to specify rescue root=root, where root is your root partition, such as /dev/sda1.
If you have just performed a diskless install on a BVM or Motorola VMEbus machine: once the system has loaded the tftplilo program from the TFTP server, from the LILO Boot: prompt enter one of:
b6000 followed by Enter to boot a BVME4000/6000
b162 followed by Enter to boot an MVME162
b167 followed by Enter to boot an MVME166/167
Go to the directory containing the installation files and start up the Penguin booter, holding down the command key. Go to the Settings dialogue (command-T), and locate the kernel options line which should look like root=/dev/ram video=font:VGA8x16 or similar.
You need to change the entry to root=/dev/yyyy. Replace the yyyy with the Linux name of the partition onto which you installed the system (e.g. /dev/sda1); you wrote this down earlier. The video=font:VGA8x8 is recommended especially for users with tiny screens. The kernel would pick a prettier (6x11) font but the console driver for this font can hang the machine, so using 8x16 or 8x8 is safer at this stage. You can change this at any time.
If you don't want to start GNU/Linux immediately each time you start, uncheck the Auto Boot option. Save your settings in the Prefs file using the Save Settings As Default option.
Now select Boot Now (command-B) to start your freshly installed GNU/Linux instead of the RAMdisk installer system.
Debian should boot, and you should see the same messages as when you first booted the installation system, followed by some new messages.