Ok, want to get this taken care of quickly? Here's the steps. But first off, have you driven another Liberty recently, ask the dealership to start one for you, and go for a ride and see if you hear the same thing. I recall the engine being rather raspy, and exibiting sounds much like you mentioned when I drove one. They are all a little noisy IMO, but perhaps yours is more so.
The most important point is to create a paper trail.
1. Write a letter detailing what the problem is, exactly when it occurs, the dates you visited the dealership, the dates/time the sounds occur and under what conditions (in the rain/morning). Do not threaten the company, ask for a solution. Threating will get you absolutely nowhere. Address it to the dealership. Provide this to the service manager at the dealership.
2. Take the same letter, readdress to to DC customer service, call them, ask the rep. to get it by fax and ask the rep. to have the District Parts and Service Manager contact the dealership, since the dealership has acknowledged there is a problem but doesn't know what to do, the District Parts and Service Manager will likely have to come down and look at the car.
3. Ask the DC customer service rep. to keep you updated on the progress. Get that rep's name, and continue to call back the same rep. Building a relationship/rapport with the same rep. will go a lot futher than talking to a bunch of different people.
4. Forget your salesperson, deal with Service Manager, and DC customer service reps.
As a side note about warranty.
DC does not have to give you a new engine. If they fix the current problem and the most cost effective way of doing so is a rebuild or part replacement, that's what they will do. Nothing you can do about it. If the problem persists, then they may replace the engine. Most likely though internal engine problems on a brand new car will warrant a replacement. Cost/customer satisfaction do count. That's why you have a warranty. It doesn't matter if you have 2km or 20000km. If there's a problem, the warranty's there for you. But if the problem still persists and they can't fix it. You have recourse. You can take them to CAMVAP and being preceedings to get your car bought back. The most important thing in one of these hearings is a proper paper trail. If you can pick up the sound on a video camera, then do that now too and store it away. Seriously, it may sound like a lot, but if you really want something solved you should do everything you can, instead of waiting for DC because you will be waiting. Secondly, dont' get upset, don't scream and yell, be civil, be helpful and be calm. What type of person do you think Customer Service is more willing to help? If you bit*h and scream, do you think the rep. or the DPSM will really feel like calling you back? I wouldn't. If your the nice person with a legitimate problem who's being civil and rational, you'll likely be at the top of the to do list. Otherwise, I'm sure the pile's pretty big, and somebody's got to be at the bottom. Be patient, give it time, but if in a month your still nowhere I'd perhaps start giving some heat to the rep., gently. That's my $0.02, up to you to spend it. But I advised a friend to do the same thing with Volvo, regarding a transmission problem, and within 2 weeks, there was a new tranny in the car. They first tried a fix, didn't work, a new transmission followed quickly and it didn't even have to go futher than the service manager. The service manager just provided the documentation to Volvo, documentation was sufficent, fix followed quickly.