There is no 'easy' way to troubleshoot anything. The number one rule is "divide and conquer". Narrow down what/where the problem is. You don't have to have an electronics degree!
Below are posts with a wealth of information, but YOU have to spend some time looking through these if you want to save your device, whether it be a TV or anything else. I tried to group these to make the search easier. With many problems, you are not the only one that has experienced the issue.
In the past couple of years there has been a increased number of threads by members that are having a problem with their RPTV. Being the oldest of the three major current technologies, of course it's understandable. Sorry to burst your bubble, but mass produced consumer products do break, no matter how much you paid for them!
Many have little electronics experience with no idea what to do other than calling someone to take a look at the set. The problem with that is,
1. You pay a fee for the visit, even if nothing is or can be done,
2. Unless you know who you are dealing with, you take a chance that he is actually familiar with the set. No, I'm not kidding.
Judging by the owners one star reviews (posted in many sites), the last point is a problem with thousands of owners where the service visit consists of someone that has no or little idea what's wrong or isn't familiar with the product (even though he should be).
Most people do not take the time to find out in advance what choices (if any) they have for "authorized" service. When the time comes, they then find there is no "authorized" shop and the manufactures tries to come up with something, but usually fails according to the experiences posted. Read through the one star reviews from Amazon.com and see all the owners that wait for the service call, shops that don't return calls or return the visit at all.
Cutting costs by manufactures (some more than others) to a point of not having a service network except in major areas and/or not having a anything at all, but telling the customer to either deal with the store where you bought it or ship it back to them at your expense. Most of those are these 'oddball' names, or 'store brands' where you have no idea what/who actually made this thing. Those you wind up 'eating' and toss and never buy again. For the 'name' brands there might be a better way.
I did a series of "Whats' Inside" threads.
For those that have no idea what's involved inside a DLP RPTV, take a look here even if your set isn't from one of these manufactures.;
Remember, divide and conquer the problem.