Missing or lost transaction and no errors to show what went wrong I have 2 missing records in SQL Server and I am trying to identify the problem that caused this issue.

New records are inserted using a stored procedure, which will return an error code to the application if something goes wrong.

The Application, SQL Server, System Logs do not show any errors during the time when these 2 transactions should have been inserted. 

How do I go about identifying the issue here? My current idea is to find a way to read the Transaction Log (from a backup restore) to see if the transactions are even in the log and if they got rolled back. 

Can anyone recommend anything else I can do to troubleshoot this? Are there DMVs or other (SQL Server hidden) logs?

I am worrying about this issue and what SQL Server did in this situation. (I have experienced issues recently with timeouts, but since a recent reboot, this problem was resolved....)
You can use ApexSQL Log to read the transaction log (online, backup, detached). Even in the trial, it shows in GUI all transactions it finds in logs. That can help you troubleshoot the issue.