You've apparently got some bogus data in your bubble memory, or maybe a problem with the bubble memory board.
If you can get the controller to boot up normally at all, get a good copy of all the parameters now (before its too late). You can manually record all the parameters from 000 to 380 or so, or you can punch them out to a PC using the serial port. If you have a serial connection to a PC, get your PC ready to receive, put the CNC into EDIT mode, press the PARAM key, then key in P-9999 then PUNCH. Once you have all the regular parameters recorded, look to see if you have any "PC parameters". These are displayed by pressing the PARAM key twice (look for "PC parameters" on the top of the screen). Manually record all the Timers, Data tables, and "Keep relays". PC parameters are only used on machines that use the Fanuc programmable controller (PC) to control all the machine interface functions. My guess is that your Hitachi mill uses the Fanuc PC, so be sure to record the PC parameters too. You can't punch the PC parameters to a computer, so you will have to record them manually.
Also, if you need to back up the part programs that are in memory or the tool offset data, this would be the time to do it. Some machines use special "Macro" programs with numbers that start with 9000 for special cycles (like tool changes) so if you have any of these, be sure that they're recorded.
Once all your data is safely recorded, you can then start clearing various sections of the bubble memory and reloading the data. You can first try to clear the part programs by holding the RESET and the DELETE key while turning the control on. If the 904 alarms still happen, try clearing out the parameter data by turning on the parameter Write/Enable switch on the main board, then pressing the red "CAN" key and the DELETE key while turning on the power. (you'll then have to re-load all those parameters). If all that fails, you can try totally clearing the bubble memory by turning on that Parameter Write/Enable switch and holding the letter "O" key and DELETE while turning on the power.
If these memory clear operations fail to stop your 904 alarm, you may have to do a complete "bubble initialize" procedure. This procedure is described in the Fanuc 6T-B and 6M-B mainenance manuals.
In any case, you've got to back up all that data FIRST!