1,2V on input pin of a 74LS273
The 74LS273 is a "Low Power Schottky" logic chip so its inputs aren't high impedance as is the case with CMOS logic.

If we look at TI's datasheet 74LS273 (the one from Motorola doesn't show this) we see input circuits:



Where you're using the Data input so it must have \$R_{eq}\$ = 8 kohm.

By itself this circuit would result in a higher voltage at the input when INPUT is connected to ground via 10 kohm so maybe your 74LS273 has a different value \$R_{eq}\$.

Anyway, the "obvious" solution is to pull down the input even "harder" using a lower value resistor, for example 1 kohm instead of 10 kohm. I'm not that familiar with LS logic (I'm more of a CMOS man) but I guess that these inputs are designed to work with open collector outputs which "pull down" quite strongly. You could consider adding a buffer to properly pull down this voltage.

Regarding ESD, I personally would not be too worried, I have never knowingly destroyed a chip through ESD either as a professional or a hobbyist. Also these 74LS chips aren't that sensitive and also have proper ESD protection. The easiest way to check is to try a different IC of the same type or a different input on the same IC, if that (input or chip) behaves the same, your chip(s) should be OK.