Your fuse link is probably not large enough. With no loses the 3500watts will draw around 285AMPS from your battery bank.
It will take a rather large battery bank to produce 12VDC at 285AMPS plus loses for any length of time.
One of my experiences was with a 1500WATT PSW Inverter running some HP TEST EQUIPMENT from the trunk of a rental car. INVERTER was connected directly to the single rental car battery terminals. The TEST EQUIPMENT added up to just under the 1500WATTs. It lasted about 15 minutes before going dead. This was with the rental car motor running...
I would look at some battery specs and look at the RESERVE POWER. i.e. two 6VDC Trojan T105 batteries in series to give you 12VDC will only produce 12VDC @25AMPS for approximately 447 minutes (7.45 hours). If you want to keep using these batteries you will have to not let them get discharged to 0% charge state before recharging so you can really only count on using them for only 4 hours in this situation.
This is a long way way from the 285AMPS current draw. If Two batteries give you 4 hours of use time, 2 more added will give you 50 AMPs capacity, etc etc etc...
INVERTERS are very BATTERY hungary
just saying...
Roy Ken