;====================================================================;
; Firebird OS Bootsector ;
; ;
; Simple bootsector written in assembler for Firebird OS ;
;====================================================================;

BITS 16
ORG 0

jmp bootsect_start ;Jump to the main code
nop

;-----------------------------------------------;
; DISK DESCRIPTION TABLE ;
;-----------------------------------------------;

OEM_ID db "FIREBIRD"
BytesPerSector dw 0x0200
SectorsPerCluster db 0x01
ReservedSectors dw 0x0001
TotalFATs db 0x02
MaxRootEntries dw 0x00E0
TotalSectorsSmall dw 0x0B40
MediaDescriptor db 0xF0
SectorsPerFAT dw 0x0009
SectorsPerTrack dw 0x0012
NumHeads dw 0x0002
HiddenSectors dd 0x00000000
TotalSectorsLarge dd 0x00000000
DriveNumber db 0x00
Flags db 0x00
Signature db 0x29
VolumeID dd 0xFFFFFFFF
VolumeLabel db "FIREBIRD OS"
SystemID db "FAT12 "


;-----------------------------------------------;
; MAIN CODE ;
;-----------------------------------------------;

bootsect_start:

mov ax, cs
mov ds, ax ;Set data segment to where we're loaded
mov es, ax

mov byte [bootdev], dl ;Save boot device number
;NOTE: A few early BIOSes are reported to improperly set DL

mov eax, 0 ;Needed for some older BIOSes

.read
mov ax, 9FE0h ;ES:BX = 9FE0:0000
mov es, ax ;
mov bx, 0 ;

mov ah, 2 ;Load disk data to ES:BX
mov al, 1 ;Load 1 sectors
mov ch, 0 ;Cylinder=0
mov cl, 2 ;Sector=2
mov dh, 0 ;Head=0
mov dl, [bootdev] ;Drive=bootdev

int 13h ;Read!
jnc .read_done ;Read went ok => continue

call reset_floppy ;ERROR => reset floppy
jnc .read ;Floppy reset OK => try again

mov si, disk_error
call print_string
jmp reboot ;Floppy reset error => reboot

.read_done
jmp 9FE0h:0000 ;Jump to the program


;-----------------------------------------------;
; DATA ;
;-----------------------------------------------;

disk_error db "[!] Bootsector: Error: Floppy error!", 0Dh, 0Ah, 0
reboot_str db "[+] Press any key to reboot...", 0Dh, 0Ah, 0
bootdev db 0 ;Boot device number


;-----------------------------------------------;
; FUNCTIONS ;
;-----------------------------------------------;

reboot: ;Reboots the machine
mov si, reboot_str
call print_string
mov ax, 0
int 16h ;Waits for keystroke
mov ax, 0
int 19h ;Reboot the system

print_string: ;Output string in SI to screen
pusha
mov ah, 0Eh ;int 10h teletype function
.repeat:
lodsb ;Get char from string
cmp al, 0
je .done ;If char is zero, end of string
int 10h ;Otherwise, print it
jmp short .repeat
.done:
popa
ret

reset_floppy: ;IN: [bootdev] = boot device; OUT: carry set on error
push ax
push dx
mov ax, 0
mov dl, byte [bootdev]
stc
int 13h
pop dx
pop ax
ret

;-----------------------------------------------;
; END OF FILE ;
;-----------------------------------------------;

times 510-($-$$) db 0 ;Pad remainder of boot sector with zeros
dw 0AA55h ;Boot signature
    

Starting address    Ending address    Content
00000                 003FF               Interrupt Vector Table
00400                 004FF               BIOS Data Area
00500                 07BFF               FREE MEMORY!
07C00                 07DFF               Boot Sector
07E00                 9FBFF               FREE MEMORY!
9FC00                 9FDFF               Kernel
9FE00                 9FFFF                Boot Loader
A0000                 BFFFF               Video Memory
C0000                 C7FFF               Video BIOS
C8000                 EFFFF               BIOS Shadow Area
F0000                 FFFFF               System BIOS
    

you can simplify with this equation:
bootloader = bootsector
kernel = 1000h:0

no need to check, if it happen to don't work, it just means there is a problem, and check for problems will not solve it not help to solve it.

for example, if your checker says, problem, unable to load kernel, it just means that you should first do a good loader, tested, and tested again, ones it works, it works.

you just have to load kernel sectors to a location and jump to (or call) it.

For starters the GDT size (line 161) is wrong. It should be gdt_end-gdt-1. And by the way, the comment is wrong as your GDT has 3 descriptors, i.e. 24d/0x18 bytes.

100c100
<       mov ax, 0x9c0       ;ES:BX = 1000:0000
---
>       mov ax, 1000h       ;ES:BX = 1000:0000
122c122
<       jmp 0x9c0:0000      ;Jump to the program
---
>       jmp 1000h:0000      ;Jump to the program
    

118,120c118,120
<       mov si, gdt+0x9c0*16                    ;start of GDT table into SI register
<       mov di, 0x500   ;locate GDT at 500h in memory
<       mov cx, gdt_end-gdt     ;size of the GDT (defined my fancy footwork)
---
>       mov si, gdt                     ;start of GDT table into SI register
>       mov di, [gdtbse]        ;locate GDT at 500h in memory
>       mov cx, [gdtsze]        ;size of the GDT (defined my fancy footwork)
139c139
<       jmp 08h:protected_mode+0x9c0*16
---
>       jmp 08h:protected_mode
151c151
<       mov word [0xb8000],'S '
---
> 
162c162
< gdtbse dd 0x500               ;where GDT is located at (bootloader_end+gdt)
---
> gdtbse dd 0xA0000 + gdt       ;where GDT is located at (bootloader_end+gdt)
    

By the way, I cant understand your correction in my comment...

kernel_main()
{
}