What does error 3004 mean?

Solution 1:

Servers are unavailable (most likely due to overload). (It's not you, it's them.) 3004 shows at character selection, 37 shows at login—same conditions.

Blizzard's official response: keep trying.

Solution 2:

Error Codes & Troubleshooting

Error 12 - This is an error we're still investigating but you can workaround it by simply changing your Battle.net account password to force your account information to refresh. Once changed you can change it back.
Error 33 and 34200 - The service is undergoing maintenance, please try again later.
Error 37 - The server is full. This is likely due to us lower the concurrency cap to address an issue or error. The only solution is to keep trying to log in.
Error 24000 - Once logged in you may run into this error when attempting to start a game. We're aware and are working to resolve it as quickly as possible.
Error 3003 or Error 75 - Click Options, under Account change your region to The Americas. The open beta is only being held on US hardware.
Error 3004, 3006, 3007, or 300008 - These are all related to timeouts or creation errors for characters or games. These are server-side issues, and need to be resolved on the game side. There are no workarounds for these errors except to try again.
Error 315300 - If you're sure you're typing your correct account information, check to ensure no additional spaces were added before or after your email address. If you're still running into this issue there may be an error in your foreign language appdata files. Some players have found a workaround but please be aware the steps they provide are not something we can currently support.
Gray login button - You need to use your Battle.net email address as your account name. Your BattleTag is a nickname, not your account name.
No Licence Attached - Please add a Battletag to your account from here
Updating Setup Files - If you're stuck on "Updating Setup Files" try these troubleshooting steps.
Crashes - For any crashes please visit the Technical Support forum or Mac Technical Support

Tips

Please remember to get and use the beta client, not the pre-download retail client
It's best to let the launcher finish the entire download before you login to avoid potential issues
During the stress test, lag and connection issues may occur
Please do not change languages in-game. This functionality is not working correctly yet and will cause the client to crash
This is an open stress test – not a demo and certainly not a finished product. You may experience a number of issues and errors, but this is exactly what helps us to prepare for the smoothest launch possible on May 15

Source: The Blue from Battle.net forums

Solution 3:

Try "spam-clicking" the start button. As in, clicking start, then hitting the enter key immediately after the error pops up; repeat. I can't say it is what the folks at Blizzard would want/recommend (can't find an official response), but it is what others seem to be doing with some degree of success. Possibly because the servers may able to support more players, but the login process maybe demands a bit more resources all at once, when compared to simply keeping you playing once already in-game?

It worked for me the one time, but this is my first time logging in after downloading all weekend. Good luck.

Diablo error 3004 - Forums - Diablo 3