The gears make a huge difference, particularly off the line.
The '94-95 LT1 engines are controlled by the Powertrain Control Module (PCM). It's a PROM (Programmable Read Only Memory)-based piece of electronics that manages all of the fuel and timing events for the engine. The PROM (or EPROM - erasable programmable read only memory), as the name implies, is programmable. There are different types of PROMs - early ones are actual chips, later ones are components soldered to a circuit board. With the advent of PROM-based PCMs, auto manufacturers could use the same piece of hardware to control virtually any drivetrain that they manufacture. They "burn" the PROM with information about that vehicle's specific configuration (engine, transmission, weight, axle ration, options, etc) and pop it into the PCM. The PROM is the "chip" you posted a picture of. In the early days, you would get one custom burned for your application. I had a glovebox full of them in my Grand National - one for street 87 octane, one for street 100 octane, one for the track 110 octane, one for the track 114 octane, one for the street 93 octane w/ alcohol, etc. and so on. I would leave the cover off the PCM so I could swap them out easily.
Eventually I moved to a FAST (
http://www.fuelairspark.com/) system in the Grand National which is a lot like modern PCMs - they can be reprogrammed over and over again using a laptop and don't have "chips" in them anymore. If I wanted a specific tune, I would flash the PCM with the laptop - it would take about 15 seconds. Run it down the track, check the logs, make adjustments and upload them to the FAST module. This is a good segue into what our Cadillacs have in the way of PCMs.
I haven't taken our Cadillac PCMs apart, but based on Jay's response and my own observations, I would assume that our PCMs have EEPROMs in them. EEPROM is defined as Electronically Erasable Programmable Read Only Memory (EEPROM). The EEPROM is soldered to the circuit board and can be electronically erased and reprogrammed over and over again. It makes it even easier for manufacturers to use the same PCM in a wide range of vehicles. They just "flash" it with vehicle-specific information and pop it in. There are "tuners" for just about every vehicle manufacturer these days that will flash your PCM for you in order to increase performance, eliminate emissions checks, etc. There are also DIY software packages that allow you to upload information to the PCM yourself. On my '96, for example, I tuned out the AIR pump check so the SES light would stop coming on once the pump failed. I also changed the temperature at which the fans come on so it ran cooler.
As an aside, our computers *might* have a CALPAK or MEMCAL chip in them. It is an actual chip that has default, limp-mode fueling information in the event the main computer fails. Not sure when GM stopped using those. I think that's what Autozone is showing you, actually. EDIT: I pried open an extra '96 PCM I have and it does not have any sort of removable chip in it other than the knock sensor module.
This guy has lots of information on LT1 and LS1 tuning:
http://www.lt1pcmtuning.com/
Back to your issue: you can't really check the PCM for faults. You can send it to a tuner to see what's been changed vs. stock, but in order to do it yourself you'd have to invest in software and cabling. I doubt the PCM has failed. You can have it put back to stock, but if the previous owner has had it reprogrammed to eliminate certain emissions equipment, and has removed that equipment, then you're going to get a Service Engine Soon light when the stock programming looks for that stuff again.
I think you should be looking beyond the PCM for your issue, particularly if the program you have had been working fine in the past. Something has failed that is causing it to run poorly.