I'm going through the exact same thing with a 74LS02 in a Tomcat special solenoid section. I thought it was a capacitor issue because the problem only cropped up after about 5-10 minutes of being on... but I swapped in a SN7402N and sure enough, I can't reproduce the issue now (on the bench at least).

Ed from GPE said 74S02 will work, so I've got a schwack of those on order. I also have a bag of 74LS02s which I'm going to stay away from. But I also have some 74HC02s which I though would work, but are giving me as much grief as the 74LS02s.

What really confuses me is the behavior indicated by probing with a logic probe. The old 7402 seems to deal with the signals on the inputs differently. I'm still trying to wrap my head around it, but I'll post a follow-up with my findings.

I knew the 74LS02 was too low, but I didn't realize the 74HC02 was even lower! Sheesh. Well, once again, I'll be sitting by the mailbox for my GPE order!