Having finally taken the time to think this scenario through, after it bobbing to the surface of my consciousness from time to time for ages, it turns out there's a lot of think about. More than enough for a separate thread. I'll have to write a Post-Apocalyptic novel!
If all normal electrics were broken, where would some survive?
(I should say it's disputed whether all electrics would be permanently broken by carpet EMPing, although most (credible) opinion leans that way. You get some absolute imbecile opinions when you look things up on the internet these days, as everyone is using it loads. I found people saying diesel engines' spark plugs need batteries, which would be taken out by an EMP, for instance.)
down mines or similar
obviously some military stuff, which is shielded, or on a submarine. Although submarines can be attacked, including by nuclear torpedoes and depth charges.
inside bank vaults, or probably mega corporations have some shielded rooms
on ships far out at sea
perhaps in very remote areas on land (Arctic Siberia etc.), if there are no explosions close enough
maybe in the bunkers of preppers who have spent a lot of money on legit shielding
I remembered that the British Army had stayed with an old engine model for its Land Rovers, as it is more robust/simple/easy to maintain and repair in field conditions etc. I checked and indeed they are still using a 1994 model engine, which will work without electrics.
Tanks' armour gives them a good degree of protection from EMP, but it would be overpowered by a close- or powerful-enough blast. I think researchers are also developing EMP tank rounds and artillery shells.
I know Challenger 2 tanks, which is the current British Army tank, although they are about to be replaced, have manual backup systems so the gunner can aim and fire if the electric systems are broken. However the (diesel) engine won't work without electrics.
I checked two other random Army vehicles to see if their engines would run without electrics, and they won't.
Mastiff Protected Patrol vehicle
Heavy Equipment Transporter (HETS)
We're not in the Cold War with the USSR any more, and the British Army isn't exactly the top dog it once was, but even the Army not having EMP-proof vehicles is rather dismaying.
I suppose if you had some electric items which worked, the thing to do would be to set up some kind of water mill which charged big batteries. You could run cables a limited distance from there (to light buildings for instance) and carry smaller batteries back and forth. You would run out of diesel for a generator sooner or later, even if you could maintain it to keep it working. You could charge batteries with windmills, or a horse walking on a treadmill, or a person pedalling an exercise bike lol, but clearly a water mill would be better.
Again though this technology would eventually fail because people wouldn't be able to maintain/repair it, and your survivors would just have to do without electricity. You would be glad to have the mill turn saw blades for your firewood though. Cutting and chopping wood by hand is laborious.
I also realised that once paraffin and the candles people found were used up, there would be a great demand for candlemaking. Food and firewood are obvious, but people would be going through loads of candles in the hours of darkness.
Or when going into buildings with little or no natural light, in the daytime. I expect people could figure out how to make them again, from beeswax or animal fat, using cotton wicks. Mediaeval torches I think worked along the same principle, rushes drawing up animal fat. Again never depicted in any fiction I've come across. I suppose most readers/viewers would be bored by this kind of detail.