If you can connect to it via the serial cable you can run some commands documented in the technicians handbook, which allows you to see and change the local IP address, and possibly reset passwords (depending on the software version). From here you could get the controller to boot and load the latest software from a specified FTP server (search QEFCC), then all the setting will be in default including the username and password however it will need to be synced back to a valid ARID with appropriate licensing if you plan to connect any phones or trunks.
To get support that ARID would need to have valid SWA. The ARID assigned to the controller you got of eBay is still sitting in someone's Mitel account that you can't access, and you will need written permission from the account holder to have this ARID and all associated licensing moved over into your AMC domain which is a lengthy process, and it may be quicker for you to create a new ARID and assign new licences if necessary.
To raise a new ticket with Mitel I would normally log into Mitel connect, then tech central tracker link then create new ticket against the ARID of the Mitel equipment in question. Much easier the phoning up as you can easily add in and attach all the details which is difficult to relay over the phone.
Instead of buying an old 3300 shell I found it easier to load a virtual 3300 vMCD in a VMware environment on my laptop, it's virtually the same thing [emoji23]