Well, when I worked at a computer shop repairing/assessing/appraising thunderstruck computers for an insurance company, more often than not it was a hopeless dance to get things to work well. This was in the late 90s, early 00's, we got shipped the insurance companies clients computers after thunderstorms and we were to assess the damage and cost for repairs, appraise the computer and if the repairs was markedly under the value of the computer we were to repair it and ship it back to the customer (and invoicing the insurance company the cost for repairs and parts), if the cost for repairs was more than the value of the computer we asked the insurance company to reimburse the whole computer for the client.
The process usually went like this: Got a thunderstruck computer to check out, first thing was to put in a new PSU, just to find out some parts of the motherboard/logic board was toast as well (sometimes completely dead, sometimes booting but giving sporadic errors). Got a spare motherboard or a computer with the same CPU and RAM sockets (we had computers with most kinds of sockets and RAM types), put in the CPU and the RAM in the testing machine only to find that the RAM had some errors in them as well. Ah well, other RAM sticks and the affected CPU seems to work fine.
Checked the Graphics card from the clients computer in the testing machine, well, seems to be a dead VGA port, oh well, a new graphics card as well. Right, the clients router died at the same time, best to check out the NIC, well, seems to be toast as well, damn it...
It was quite unusual to find a computer that was killed by a nearby lightning strike that actually only had one or two defective parts. But it did happen, I'm not saying otherwise.
Sometimes we had machines which worked flawlessly by just replacing the PSU and sometimes we had machines that we replaced the PSU on and it seemed to work OK, until you heard from the client 4 weeks later that the computer locked up a few times a week (which hadn't happened before the thunderstrike).
After a while we learned it was easiest just to regard them all as toast and chuck them in a electronics recycling cage and ask the insurance company to reimburse the client for the whole computer instead of trying to repair theml.
I'm just saying to be prepared to start unraveling a chain of defective parts. But you could be lucky and only the PSU and/or the Logic board is toast (if the Logic Board is toast, most likely the PSU is as well).
I'd start with the PSU, I'm guessing there is more than one rail of power and the "constant power" is some sort of standby power to allow for the power switch to actually work (much like how an ATX PSU works). I've had more than one occasion on PCs at least were the PSU is dead but still making testing lights on the motherboard light up.
