Try the "Player API Client". I think this was the solution to my friends problem, though I can't remember real well. If this doesn't work I'll keep thinking of what I did to get my friends up and running.
Its one of 2 things. Are u using modloader? Did you delete the meta file? Are you using the correct optifine? When the client comes up force update by clicking options and start fresh. Download the newest modloader from the minecraft forums. Copy modloader files into your .jar. Make sure you delete the meta folder that prevents the black screen. Copy optifine files into .jar and start up minecraft. If done right should start up as normal. Hope this helps.
If it's just blackscreen, try deleting the META-INF file in minecraft.jar If you get an error report please tell me which mods you have installed and if possible a copy of the error report.
