It's ridiculous, but I would still just be inclined to settle and get on with life rather than fight (of course, negotiating for lower price or split cost of repair if possible).
If the appliance is listed in the inventory, then it's usually the landlord's job to fix it if it breaks. Check what your lease says. Of course if the damage appears to be caused by negligence on your part - say a smashed stove top or something, then fair enough. But a fault with the appliance provided by the landlord, is usually fixed by the landlord.
Tip for the future - when doing the handover inspection with the landlord photograph everything with time / date stamps. It might not stop the landlord trying it on, but likely gives you a much stronger claim against the landlord and you can threaten to use it as evidence in a small claim.
It really depends on how much is your time cost and whether you want justice over money.
If you want justice, you need to spend your time to prepare a statement of claim. Be prepared to answer unexpected question from the court.
If you want money, negotiate with the Landlord on the ground of depreciation in value of appliance over time. It would be difficult to proceed further if you have no information on the appliance at the time of handback of the property. Try to work out with the Landlord for a fair amount of deduction and get back the balance from the Landlord ASAP.
I had been a residential leasing officer as my profession acting on behalf of the Landlord but we did it professionally via having a proper record of handover and handback conditions duly signed by the Landlord and the Tenant.
Why dont you just tell the landlord that the water heater is the fixture of the apartment, and if it breaks through normal wear and tear is always landlord responsibility to fix, just like aircon, oven, water taps, or anything else in the apartment provided to you by the landlord at the time you move in. So you should get the full $31,000 deposit back. Have you said this politely to landlord? I am curious to know what kind of response the landlord will give to this, because to me its such a simple open and shut case that a tenant would never have to pay for something like this.
I really dont like the idea of fighting in court etc like everyone else, but this is so openly obvious that LL would lose, and they must know this if they had even half a brain. Polite but firm "Sorry but the water heater is clearly your responsibility" might knock a bit of sense into them without having to go to court.
I find it a bit strange people are suggesting to get other quotes on water heaters, negotiate on depreciation, etc. This whole area completely landlord responsibility. You pay landlord $2m rent over 6 years for them to deal with this shit and take care of the things that break normally.
Landlord has keys plus deposit. That is a situation you never want to be facing.
I'm not too clued up on banking, but does issuing a cheque have any bearing? Does that cheque still have any value for the OP or is it just a piece of paper now?