Thanks - I have been corresponding with PB Tech for some time and I will take it back if I can’t source the screws myself. It’s not going to be easy for me to get it back there so if I can fix the noise with a couple of screws, that would be preferable :) 

The "normal" drive securing screws have the same thread as the case screws but the typical drive securing screws are only 5-6 mm long.

So, yes, as the OP has stated, a longer case screw is what is needed if there is a gap that needs to be bridged.

Most of us have heaps of the short screws but I don't have a couple of case screws that would suit.

andrewNZ: I've reread your OP.
You purchased this in January from PB.

Just take the the whole machine in for a warranty repair. Make it their issue.

If I owned PBtech, built a pc for a customer, and forgot to install some screws... I'd say, bring it in, we'll put them in right away while you wait.  So sorry we stuffed this up. 

This is terrible service from them. 

Yes, the after-sales service hasn’t been great. I would have been happy to pop in and pick the screws up but they claim not to have any of the right length. 

@linw, you have hit the nail on the head. Someone is very kindly trying to source me some, but would you mind confirming the name of the screw in case they are unsuccessful and I need to order them online? Do I need 6-32 UNC screws?

Where are you located? I can check my box of screws and see if some would fit. I am in AKL CBD.

Wikipedia is on your side with 6-32 UNC.  It says used for securing a 3.5-inch hard disk drive to the case.

Good luck - something will click for you.

littleheaven:

 

Yes, the after-sales service hasn’t been great. I would have been happy to pop in and pick the screws up but they claim not to have any of the right length. 

 

Then, I'd admit to an even bigger 'screw up', and provide a new case or whatever is necessary. 

If they don't have screws of the right length, why are they even building PC's? 

CrashAndBurn:

 

Where are you located? I can check my box of screws and see if some would fit. I am in AKL CBD.

 

andrewNZ: Actually, I don't mean to offend anyone here, but I feel like the screw up is trying to get them to supply something very specific. They may very well not have that specific thing you're asking for, and what you're asking for may not be the best solution.
The drive bays might be, as previously mentioned, toolless bays.
They might be missing rubber mounts.

You need to get them to diagnose and fix the issue.
Just tell them, "This has noisy vibration when running, please fix under warranty"

Making them fix it also helps with other potential warranty issues later.
They can't say you messed up the drive mounting.

Oh, no offence taken. I realise that this is the ultimate resolution, but it's going to be logistically very difficult for me to get it back to PB Tech. Also, the buzzing was intermittent - it fine some days and noisy on others. They might not be able to replicate it immediately and I don't really want to run the risk of them claiming nothing is wrong with it and charging me an inspection fee. Rest assured that if I cannot resolve the problem, I will absolutely take it back.