Here's the deal -
The 552T DOES have an input, unfortunately, it's a single "-" pulse though - can't be programmed to a sequence of 2 or 3 pulses like the later models. So, theoretically, you could hook it up to your OEM fob in two ways:
1) Hook the appropriate wire to the door locks. Problem: Every time you lock your door, the starter will engage. Hardly useful IMO.
2) Disconnect the harness to the rear glass popper and connect the wire to that circuit. You'd use the rear glass button on the OEM fob to start. Problem: You can no longer pop the rear glass with the remote. IMO, not a huge deal. I never hooked this up on mine because I have been lazy about it, and I don't even miss that feature. When you unlock/open the tailgate, the glass opens, and if you want just the glass to open, pull the handle gently. I think this is a feasible solution to your problem.
The only other solution is to buy a DEI fob - get one off ebay. Of course DEI will direct you to an authorized reseller. I am not sure if the later model more rounded fobs would work, but they may (I'd think the 551R may work. I don't think the 562T fob will work). The 552T that I had was very square and just had two grey buttons labeled "I" and "II". "I" would toggle lock/unlock/. "II" was for an aux output - i.e., an alarm or something (you won't use this feature). Pushing both would start the vehicle.
HERE is the DEI installation guide.
P3 shows the various wiring harnesses. You're looking for the white/blue on the H1 harness
P15 better describes the functionality
P36 shows how to add a remote (if you buy one)
P38 starts the section on the options you can program.
To program, there should be an LED on the actual brain. Additionally, you'll need a momentary switch hooked up to program. Hopefully your installers were good and left the one that came with it. Chances are they probably didn't though - PC jumpers and connectors can be used to make a harness, and a cheap radio shack momentary switch will do. It's not impossible to add fobs and program features, but it's not extremely easy. I find that unit to be harder since the LED is sitting on the brain and you have to be a contortionist to get under the dash and watch the light flash for programming.
Good luck! If you need any help, I'll give it my best shot. the12volt.com is a great resource too.