This issue probably has NOTHING to do with patching the QC/ALM-Server.

Look int he SA log.
I bet you will find something that looks like this:

**Error; Failed to obtain a connection to schema 'default_almdemo_db'**

Normally, ALL QC-related Oracle Schema-users have STATIC / never expiring passwords or this type of issue will occur.
My guess is that you created these ''not-opening'' projects about 90 or 180 days ago -- the default password expiration setting in Oracle.
When you create a new project in QC, IMMEDIATELY have the DBA set the schema-user's password to NEVER Expire.

The other rule of thumb is to have ALL schema passwords in Oracle be the same password string for convenience.
When you create new projects (QC creates new corresponding schemas in Oracle), it will assign the same ''default'' password to them as it creates them.

The easiest thing to do would be to have the DBA re-enable the expired schema-user passwords and set back to their original password. This way, your stored password strings in QC will still be honored and the project(s) will start working again.