Linden Lab Official:I bought Linden Dollars (L$) but my balance hasn't updated!
If you bought Linden Dollars (L$) through the LindeX, they should show up in your balance more or less instantly. So if they don't appear instantly (or after a reasonable wait time), something may be wrong.
As a first step, you may want to check the Second Life Blog to see if we're already aware of the problem and working to fix it. Chances are good that if it's something that affects a large number of Residents, we're already on it.
If it looks like a problem that only affects you, you should probably file a support ticket.