Jump start car with AGM battery
Probably that battery is not designed for automotive applications. 

SLA (Sealed Lead Acid) batteries are designed to start car engines, and that requires a peak current that may be several time the C rating of the battery. 

For example, a SLA battery having 43Ah capacity (and hence a C rating of 43A) could provide a max current of 390A for a couple of seconds (I'm looking at that specific one right now, if you wonder why those not round numbers):







The fact it has an integrated fuse with such a low rating could mean that it is a battery meant for "deep discharge" (deep-cycle batteries) applications, i.e. for providing an energy reservoir in applications such as UPS systems or emergency lighting system or the like. See this page on batteryuniversity.com. Excerpts:


  Starter and Deep-cycle Batteries
  
  The starter battery is designed to crank an engine with a momentary high-power load lasting a second or so. For its size, the battery is able to deliver high current but it cannot be deep-cycled. Starter batteries are rated with Ah or RS (reserve capacity) to indicate energy storage capability, as well as CCA (cold cranking amps) to signify the current a battery can deliver at cold temperature. SAE J537 specifies 30 seconds of discharge at –18°C (0°F) at the rated CCA ampere without the battery voltage dropping below 7.2 volts. RC reflects the runtime in minutes at a steady discharge of 25. (SAE stands for Society of Automotive Engineers.) See also BU-902a: How to Measure CCA.


Usually deep-cycle batteries have a lower peak current rating than a starter-battery of comparable capacity. 

Anyway, the presence of that fuse tells you that you can't possibly start a car with that battery. Even a small car needs a starter-battery with at very least ~10Ah capacity, this means it should be able to deliver a peak current of at least ~50A (and I'm toning it down; actually in all my life I've never seen a car battery having less than 30-40Ah rating).  

Bottom line: to jump start a car you need a (possibly fully-charged) starter-type SLA battery having an Ah rating comparable with the battery mounted on the car, so that it can survive the couple of minutes you need to enter your car and start the engine and still provide the peak current needed by the starter motor during the start phase.

Maybe you could attempt a jump-start with a deep-cycle battery, but probably it should have a capacity several times the one installed in the car. Say 200Ah for a car mounting a 50Ah battery. You are in for heavy-weight lifting!

Anyway, if you posted a photo of that battery it might help to narrow down the issue and give you a more accurate answer.