I am quite surprised the laptop would not start.
What is it?
Off the top of my head, I can think of 4 Macs all using the 'high power' wall wart, at least 2 that ran fine with the 'low power' wall wart, 3 Toshibas, and another I can't recall, that run fine from seriously cheap inverters
(175W and 400W Vectors, 150W Freedom Jazz, {150W PROwatt is not cheap but does the job on the ones it was subjected to}).
In fact, I never saw a laptop that would not work from the 400W Vector.
The sump pump doesn't surprise me at all.
I have use a 1200W transformer based inverter rated for 200% overload for 5 minutes, powered by the running truck battery, and bring a 1/4HP sump pump just in case.
If the head is high enough, and if the pipe is that 1.25" corrugated, and its a 3/4 or 1HP pump, it might not start reliably.
Could be the #7 jumper cable connection, made of both halves of $4 #10 Big Lots jumper cables.
I never thought about a gas dryer. Ours (grid) dims the basement lights for a full second until it is up and running. It must be quite a large and long drain.
If the grid is down, and I only have two 8-Ds available, my order of priorities would be security, communication, fridge/freezer/water level, and light somewhere in there.
Clean dry jeans do not make the list.
"The basement is flooding, the food is spoiling, and the com lines are down, and a load of laundry needs done right now."
Heat from a battery bank is pretty silly in the overall picture.
Your room heater = 1500W.
My wife's hair dryer = 1850W, and it doesn't make the house warm.
If it is so cold that bit of heat for a short time makes any difference, time to start the gas oven, or burn the furniture and keep the internet/TV connected.
I am just saying when the poo hits the fan, the priorities change fast.
Niles OH tornado of '85 with the substation next to the roller rink completely MIA for >2 weeks, and a hurricane parking over us for a few days about 7 years ago, and my #1 priority is now the sump pumps.
G-