hmmm, you really need an oscilloscope here to see if the LTC is actually outputting anything. i'd be very surprised if the LTC's are actually dead, unless you've somehow reversed the power inputs with a fairly large input voltage. If that was the case then it would never have worked at all. Are you sure you're not trying to run the PS1 at a clock rate that makes it crash? Try turning it on with the LTC pot set differently, and check that you definately have the LTC soldered in the correct way round.
It could be that what you're thinking is a steady voltage to power the LTC is in fact all over the place, but your multimeter isn't fast enough to register it, assuming you are using a multimeter. I take it the PS1 doesn't have a voltage regulator to source a steady 5v?
What voltage does the PS1 run on? If its over about 7.5v or so, you could always hook up your own 5v regulator.
If the coil is still in place when you are soldering in the LTC you may find that its all very unstable and you might need to just remove it completely.