ORA-12505: TNS:listener does not currently know of SID given in connect descriptor
As the ORA-19815 message indicates, your 3GB recovery destination is full; the database is unable to archive any more redo log files. It has reached a point where it needs to switch a full redo log file out, but there are none available for re-use because they can't be archived. I imagine this is why it wouldn't shut down cleanly, and possibly why you wanted to shut down in the first place as you wouldn't have been able to do much with the database in that state.

The short-term fix is to increase the size of the recovery area, assuming you have enough disk space, e.g.:

startup nomount
alter system set db_recovery_file_dest_size=4G scope=both;
alter database mount;
alter database open;


But you then need to work out how to manage your archives, and set the recovery area size to a sensible value for your backup and retention needs. This may be as simple as scheduling a job to remove obsolete backups, e.g. from the Enterprise Manager console's Availability tab, under Manage Current Backup; but you need to determine the best course for you (and not blindly follow advice from some random guy on the Internet who knows nothing about your requirements, and not that much about EM/RMAN either).