Identify the DVD chip using the Wii’s serial number
Apparently the firstgen modchips are not compatible with all of the Wiis made to date, as some have a different DVD chips in them… You can use this table to check your serial number against to see if you can buy a firstgen modchip or if you should wait until the next generation comes out.
via ps2-scene

Forget about the purchase date or the checksum digit in the box.
It seems the first part of the serial number holds the key to knowing if you have the incompatible D2B chip or not.

Check your serial number against the tables below.

Europe

GC2 - DMS or GC2R - D2A (Compatible with first generation mod chips)
- LEH 100XXXXX
- LEH 101XXXXX
- LEH 102XXXXX
- LEH 103XXXXX
- LEH 104XXXXX
- LEH 105XXXXX
- LEH 106XXXXX
- LEH 107XXXXX
- LEH 108XXXXX
- LEH 10812XXX
- LEH 1085XXXX
- LEH 1091XXXX
- LEH 109166XX
- LEH 10979XXX

GC2R - D2B (Incompatible with first generation mod chips)
- LEH 10889XXX
- LEH 109225XX
- LEH 1100XXXX
- LEH 1101XXXX
- LEH 1104XXXX

For European models it seems the D2B chip was introduced somewhere between LEH 1091XXXX and LEH 109225XX.

North America

GC2 - DMS or GC2R - D2A (Compatible with first generation mod chips)
- LU 100XXXXXX
- LU 101XXXXXX
- LU 102XXXXXX
- LU 103XXXXXX
- LU 104XXXXXX
- LU 1050XXXXX

- LU 300XXXXXX
- LU 301XXXXXX
- LU 302XXXXXX
- LU 303XXXXXX
- LU 304XXXXXX
- LU 305XXXXXX
- LU 306XXXXXX

- LU 502XXXXXX
- LU 503XXXXXX
- LU 504XXXXXX
- LU 505XXXXXX
- LU 506XXXXXX
- LU 5074XXXXX

GC2R - D2B (Incompatible with first generation mod chips)
- LU 1047XXXXX
- LU 1054XXXXX

- LU 3072XXXXX

- LU 50853XXXX
- LU 5089XXXXX

For North-America it appears that there are three different ranges in use (LU1/LU3/LU5).
Its possible that each range is used in a different area, factory or language pack.
Each range will have a number where the D2B chip is introduced.
For LU1 this seems to be between LU 104XXXXXX and LU 1054XXXXX.
For LU3 its between LU306XXXXXX and LU3072XXXXX and
for LU5 its somewhere between LU 5074XXXXX and LU50853XXXX.

Australia

GC2 - DMS or GC2R - D2A (Compatible with first generation mod chips)
- LAH 10067XXX

Japan

GC2 - DMS or GC2R - D2A (Compatible with first generation mod chips)
- LJH 102XXXXX

GC2R - D2B (Incompatible with first generation mod chips)
- LJH 1038XXXX