Well, we have to tackle this in stages using what you do have, and might scrounge.
First a decent paper clip we can cut/mod to make into a solid bridge wire.
Then,
We can short the 8mhz and clk output wires on the plug to restore 8mhz.
That is your green and white looking wires next to the red one.
Just make vitally sure they are correctly connected.
(You green is either 16mhz or 8mhz easy to see- but you have 3 white... triple check)
You will notice my pin out 'overlay' diagram in the instructions reflect this.
Then the original FDD should finally return to normal operation.
It has to- this mod board we're putting in is only to select a clock. Those other wires are going nowhere now
with it removed. We've restored our 8mhz signal/cut.
No need to do anything other than unplug the mod board and attempt to get the 720k FDD working
by restoring the 8mhz clock through the added wiring via a jumper.
Leave pin2 connected and such. No affect in this situation.
At this stage it should be back to normal. Try the new FDD too. If DS0 jumpering is ok.
Success?, We could perform
another test. (Leave the jumper in place)
I'd leave the now connected? 1.44MB drive, still
without the mod connected.
I would clip on lead of the MM in DC mode to the exposed and twisted pin 2 wire, and the other to gnd.
Power up the ST.
Expect to see about 5v immediately with no or a HD disc inserted. Then basically gnd or 0v with a DD disk. (Maybe a few mV)
Try again with the mod connected. (Why because its' pull down resisters load the pin2 line)... obviously remove the jumper.
Now we will know if the switching signal is working. (We're not even trying to really boot here- just testing)
Check again at pin 10 of the chip, hi/lo changing as the DD disk is loaded and unloaded.
Is pin 9 at Gnd?... should be- its unused HDD1.... Also DS1 Pin 11 needs to be 5v at all times too. Unless B: is used.
Additionally, check power is getting to the mod, 5v at pin 16. And even a minor check across the chip to its gnd at pin 8.
8Mhz clock input is checkable by testing pins 2,3,4 & 14 for about 1.8-2.1v (They are all joined together- but all must work)
16Mhz clock is on pins 12,13,15 & 1. And much the same voltage suprisingly.
When checking my own mod here for
output frequency voltage on pin 5, (from inserting or removing a DD disk) I notice about 0.1v change.
Enough to notice.
These checks would show 99% of likely causes. Outside of static damage, and overheated soldering. (Both highly unlikely)
I'll offer

- for luck.
ST.
Oh, and PS..... A reminder- counting pins on the chip.... look for the dot/notch at one end. Consider the notch the top.
The pin to its left is pin 1, and we count anticlockwise down around and up, the chip. 16 pins on the LS151.
1 * 16
2 15
3 14
4 13
5 12
6 11
7 10
8 9