Well there wasn't a Windows 97. It went from Win 95 to Win 98.
https://en.wikipedia.org/wiki/History_of_Microsoft_Windows Anyway that is not the point. Your suggestion that the OP takes his computer to someone who knows what he/she is doing is the OP's next step. Before he does any more damage. As it is he could be looking at another new PSU and, quite possibly, a motherboard.
Maybe thats right, there does come a point where its impossible to define between a fault on the Board or with the PSU without a Multimeter to test the PSU, but I would still try to reset the CMOS first if I where the OP, then should that fail off to have it checked out.
Fact is you could save money at the repair shop if you know specifically that all you want them to do is quickly test the PSU, then following a CMOS reset, should your PSU check out to be fine then at that point if you still can't get the BIOS up I would simply buy a new Board. Should on the other hand the PSU prove to be faulty then you know you need a new PSU whatever so I would start out with just buying a new PSU and hope that its just the PSU thats faulty since its entirely possible that a spike can clean out both the PSU and the board in one swoop, else ether one, but since its much easier to test the PSU, assuming the OP wants to save money doing the repairs himself and has learn his lesson about attaching power rails with the system turned on so not to make the same mistake again, then I think the best course of action is as follow
1. Reset the CMOS (FREE AND EASY)
2. Have the PSU tested in a shop (I know my local shop would do that would do that for free, but I guess its who you know, and why I would buy my parts from there but 5 mins for them to test a PSU not going to cost much you would think wherever you go)
3. If PSU fail = Buy new PSU
3.1 If after changing the PSU still no joy buy a new board as well (this because you had to anyway cos if your at this stage they both fried together)
4. If PSU test pass = Buy new board because thats where you will find your fault is via process of elimination.
And yes there was a Windows 97 for a very short time, except Microsoft recalled it and did a free upgrade straight to Windows 98, ditching all support for 97 forcing all systems to be updated to 98 hence Windows 98 became just a updated version of Windows 97, just like when they went from Windows 8 to Windows 8.1, except there naming system was different back then.