Dylanjiva

Those are actually MOVISTORs, a non-linear resistor used to suppress transients. Basically, it's a very high resistance until a certain voltage is reached, at which point its resistance lowers dramatically to absorb the transient. Every time that they absorb energy, they degrade slightly, until they eventually fail.
AC-in being shorted is likely because of the MOV. These are well known, fairly inexpensive, and replaceable.
The battery terminals being shorted is usually because the MOSFETs have failed shorted. These are much more expensive and difficult to replace, although any competent repair shop should be able to do it. When they fail, these often take out some gate driver components, which are much harder to track down. Sometimes it will also take out the IGBTs, and if so, some of their gate drive components. The MOSFETs are often lined up under the edge of a heatsink along one edge of the main board. It's hard to see them without removing the main board, though you might be able to see through some ventilation holes. Burned MOSFETs are usually very obvious: blackened parts, legs blown off, cracked or pitted epoxy.
There are some capacitors that should be replaced; these protect the MOSFETs from switching transients. These capacitors drying out may have caused most of the damage, although with the MOV failure, some sort of transient due to load shedding is more likely.
As for whether it is worth repairing, that's a harder call. If you can find the right repair person, it can well be.
Note that many repair facilities these days don't do component level repairs; they will replace the entire main board, which has about 75% of the complexity of the inverter, and hence a big chunk of the cost. If such a repair is the only option, then it becomes much more marginal.

@BritishRacingGreen can sort you out 

I’ve learnt a lot from this forum through others sharing their experiences so I thought I would give back and share what I have learned.
I have a 3kW Axpert inverter connected to a raspberry pi running ICC and Emoncms. I have been frustrated with not being able to get accurate State of Charge information from the Axpert because it uses voltage to estimate SOC values which is unreliable. I have looked at getting a Victron battery monitor but held back because I was sure there must be a way to get a true SOC by using the ICC and Emoncms software to track kWh of charging and discharging from the battery. After some tinkering, I have finally found a way to get an accurate state of charge reading and thought I would share this with others.
Basically, it involves setting up some feeds in Emoncms in order to track battery kWh and then processing this feed to convert it to a state of charge percentage. This does not work if you use utility to charge your batteries as the Axpert does not seem to log this. This only works if you use solar exclusively to charge your batteries. Here are the steps to follow:
1. Create cumulative battery kWh feed:
In Emoncms go to Inputs where you will see a list of various inputs that are logged. Find the input named “batterywatts” and click the spanner icon. Click on “Log to feed” and select “Power to kWh”.  In the feed drop down box select “Create New” and give it a name such as “batterykWh”. Click add and then save. 2. Create a State of Charge Virtual feed:
In Emoncms go to Feeds where you will see a list of various feeds. Scroll down to the bottom and click on “New Virtual feed”. Give it a name such as “Battery SOC” and click save. Tick the check box next to the newly created virtual feed and click on the spanner icon on the top of the page. In the dropdown box select “Source Feed” and the select the “batterykWh” feed you created in step 1, click add. Now we need to do some maths to convert the cumulative Kwh feed into a state of charge percentage: Calculate your battery bank capacity in kWh (eg. I have a 24V 200Ah bank of batteries: (200x24)/1000=4.8kWh) Calculate the scale to convert kWh units of your battery into a percentage (eg. 100/4.8=20.8333) Set up processing steps in the State of Charge Virtual feed: To convert KWh to percentage: In the dropdown box select Calibration “X” and then in the value box put the negative of the scale value calculated above (eg. -20.8333). Click Add. To invert the percentage scale: In the dropdown box select Calibration “+” and then then in the value box put “-100”. Click Add. To make sure the percentage value is always a positive value: In the dropdown box select Calibration “Absolute Value” and then then in the value box put “100”. Click Add. Click Save 3. Zero the State of Charge Virtual feed when the battery is fully charged:
Go to the feeds page of Emoncms and select the checkbox next to the “batterykWh” feed created in step 1. Click on the dustbin icon at the top of the page and press “clear data”. Don’t delete the feed by mistake. You may need to do this calibration occasionally or after using utility to charge your batteries. 4. Now you are ready to add the State of Charge Virtual feed values to your Emoncms dashboards.
I have attached some GIF files showing the process. Hope someone finds it useful.