Unfortunately it's probably replacement territory, I doubt anyone does board work on smaller units.

This popped up on a quick search: https://www.pbtech.co.nz/product/UPSDNX1750/Dynamix-UPSG750-SafeGuard-750VA-450W-Line-Interact

MadEngineer: Throwing out equipment when all it needs is a few cents worth of electronics is the practice that's partly responsible for the state of today's world. So, $200 for you isn't a big deal? Lucky you. Start saving, otherwise you're in for a lean time when you retire. 

Radiotron: Yes, that's the unit.

Might want to confirm the battery was the right one to use as mentioned. The specs on PB say 12v as well.

Don't waste time and effort on it, just replace it

geekIT:

 

when all it needs is a few cents worth of electronics 

 

While that may be the case, the cost is in the diagnostics, ordering the items, installing the items and then testing. 

A couple of hours labour, and you have already eclipsed what it would cost for a new one.

geekIT:

 

MadEngineer: Throwing out equipment when all it needs is a few cents worth of electronics is the practice that's partly responsible for the state of today's world. So, $200 for you isn't a big deal? Lucky you. Start saving, otherwise you're in for a lean time when you retire. 

 

Radiotron: Yes, that's the unit.

 

It may be a few cents worth of electronics, but it will take time to diagnose which part, source the part, remove the old part, fit the new part, test and reassemble then test again. This is assuming the board is even serviceable. 
When I did this kind of work 10 Years ago, my time was charged out at $80.00 to $120.00 per hour with a minimum 1 hour charge.

geekIT:

 

MadEngineer: Throwing out equipment when all it needs is a few cents worth of electronics is the practice that's partly responsible for the state of today's world. So, $200 for you isn't a big deal? Lucky you. Start saving, otherwise you're in for a lean time when you retire. 

 

Radiotron: Yes, that's the unit.

 

And you've not addressed the comments here about the voltage.

My guess is that the OP put 9v by mistake instead of 9AHr?

Changing the battery is the cheapest option to confirm if there is a real fault elsewhere. These basic units tend to behave badly when the battery has failed.

k1w1k1d:

 

My guess is that the OP put 9v by mistake instead of 9AHr?

 

You're all correct, I glanced at the specs on the PBT site and typed '9'. However, I was just making the point that it was an almost new battery. Sure, these days it's uneconomic to repair equipment, but I grew up in an era when almost anything could be repaired or recycled. It was also an era when the end of our civilization was unimaginable, instead of predictable.

SB UPS12V9 12V 9.0 AH Replacement UPS Battery