u got a few choices:
1.itll require d2loader for ez doing: run through every letter + number possible...this will give u about... hmm...36 x 36 = x
x will = the amoun to ftries you have to do...if im right...
2. Scam someone for new key ***
3. Buy a new CD-Key for 15 dollars through blizzard
4. Buy a new set of diablo + lod for roughly 30 bucks**
** use the "give to store, open very carefully, get key, seal back up neatly, and return trick
*** I DO NOT INDORSE THIS IDEA AND WILL NOT HELP ALONG WITH THE FACT THAT BATTLE.NET WILL NOT HELP YOU IN GENERAL ON TROJANS
*****edit*****
there is one alternative method:
you say you gota new computer. do you still have your old one with diablo installed on it? if so theres programs that will show what your cd key and then just write it down and use it.
theres 2 programs that will help:
cd-key changer
and
cd-key shower. check stickes for either/both of them i believe