I have very bad news for you.

You should not have deleted the ibdata1 file. Here is why:

ibdata1 contains four type of information:

• table metadata
• MVCC data
• data pages (with innodb_file_per_table enabled)
• index pages (with innodb_file_per_table enabled)

Each InnoDB table created has a numercial id assigned to it via some auto increment metadata feature to each ibd file. That internal tablespace id (ITSID) is embedded in the .ibd file. That number is checked against the list of ITSIDs maintained, guess where, ... ibdata1.

I also have very good news for you along with some bad news.

It is possible to reconstruct ibdata1 to have the correct ITSIDs but it takes work to do it. While I personally have not done procedure alone, I assisted a client at my employer's web hosting to do this. We figured this out together but since the client hosed ibdata1, I let him do most of the work (30 InnoDB tables).

Anyway, here a past post I made in the DBA StackExchange. I answered another question whose root cause was the mixing up of ITSIDs.

To cut right to the chase, here is the article explaining what to do with reference to ITSID and how to massage ibdata1 into acknowledging the presence of the ITSID contained within the .ibd file.

I am sorry there is no quick-and-dirty method for recovering the .ibd file other than playing games with ITSIDs.

UPDATE 2011-10-17 06:19 EDT

Here is your original innodb configuration from your question:

innodb_file_per_table=1
innodb_flush_method=O_DIRECT
innodb_log_file_size=1G
innodb_buffer_pool_size=4G
innodb_data_file_path=ibdata1:10M:autoextend
innodb_buffer_pool_size = 384M
innodb_log_file_size=5M
innodb_lock_wait_timeout = 18000 

Please notice that innodb_log_file_size is there twice. Look carefully...

innodb_file_per_table=1
innodb_flush_method=O_DIRECT
innodb_log_file_size=1G <----
innodb_buffer_pool_size=4G
innodb_data_file_path=ibdata1:10M:autoextend
innodb_buffer_pool_size = 384M
innodb_log_file_size=5M <----
innodb_lock_wait_timeout = 18000 

The last setting of innodb_log_file_size takes precedence. MySQL expected to start up with the log files being 5M. Your ib_logfile0 and ib_logfile1 were 1G when you tried to start up mysqld. It saw a size conflict and took the path of least resistance, which was to disable InnoDB. That's why InnoDB was missing from show engines;. Mystery solved !!!

UPDATE 2011-10-17 11:07 EDT

The error message was deceptive because innodb_log_file_size was smaller than the log files (ib_logfile0 and ib_logfile1), which were 1G at the time. What's interesting is this: Corruption was reported because the file was expected to be 5M and the files were bigger. If the situation were reversed and the innodb log files were smaller than the declared size in my.cnf you should get something like this in the error log:

110216 9:48:41 InnoDB: Initializing buffer pool, size = 128.0M
110216 9:48:41 InnoDB: Completed initialization of buffer pool
InnoDB: Error: log file ./ib_logfile0 is of different size 0 5242880 bytes
InnoDB: than specified in the .cnf file 0 33554432 bytes!
110216 9:48:41 [ERROR] Plugin 'InnoDB' init function returned error.
110216 9:48:41 [ERROR] Plugin 'InnoDB' registration as a STORAGE ENGINE failed.

In this example, the log files were already existing as 5M and the setting for innodb_log_file_size was bigger (in this case, 32M).

For this particular question, I blame MySQL (eh Oracle [still hate saying it]) for the inconsistent error message protocol.

While .frm, .MYD, .MYI are enough for MyISAM, ibdata1 (InnoDB Global Table space) is needed for InnoDB even if you are using innodb_file_per_table = TRUE.

ibdata1 holds meta data for InnoDB Tables. InnoDB Table can't be found without those meta data. So you are getting "Table 'table_name' doesn't exist". error.

MySQL Manual states that

You cannot freely move .ibd files between database directories as you can with MyISAM table files. The table definition stored in the InnoDB shared tablespace includes the database name. The transaction IDs and log sequence numbers stored in the tablespace files also differ between databases.

The main reason is Table id is different both source and dest. DB's ibdata1. So ibdata1 should be moved from src to dest.