Sadly, the way to diagnose these things is to replace one thing at a time and avoid breaking things like fragile connectors until the symptom goes away. This is a losing battle for one-off repairs and why only large shops can afford to have the experience and tools / parts on hand to repair machines with symptoms that are not simple or obvious. You can't see most damage and even testing for it is usually harder than exchanging a whole component to see if it addresses the larger system issue.
Without the manufacturer knowledge and diagnostic tools, you (and I) are at a handicap at telling what is really failing and doing subcomponent repair is extremely tricky without a professional shop and dedicated tools / test rig to ensure the new logic board is functioning.
If it's worth $400 to get fixed, perhaps go back and have Apple or an authorized tech check your work and see if it's still eligible for a repair. Worst case is you have to pay the labor fee to get it looked at - in the US I believe it's $39 for labor and no parts used for any Mac repair.
I would suggest being up front with them as there are three scenarios if you admit having been inside the mac to try and fix it yourself:
- They just dismiss you as a hack and don't even look at the work to see if the mac was damaged during the repair - this is far less likely if you aren't actively deceiving the tech.
- They appreciate the honesty and can see that things are broken and might quote you to fix whatever is wrong - covering anything they can be sure was a manufacturing issue - charging you for any damage caused by whatever.
- They appreciate the honesty (and gumption to attempt a repair like that) and can see you did great work. In this case there is no damage to fix and they can just proceed with a normal repair where it wasn't worked on. You almost certainly want to have the original logic board inside the mac if there's any doubt it's the wrong part.
Having been inside the computer, you will know how well you got all the minute connectors off and back together and can appreciate how delicate and cramped the connectors and parts are inside. It's entirely possible one of the cables needs to be repaired in addition to (or in stead of) the main board. Also, what if the problem was in the magsafe board or some other part drawing too much current / blocking the communications buses to allow the machine to start. You can't know until you do all the work to isolate the issue at which point the issue is trivial to remedy.
In your specific case - being in Panama, you might have to just arrange mail in service in the US (or another country) and pay to have it shipped. Just be clear on what the charges might be for diagnosis / shipping if it turns out to be damaged or not repairable under the flat rate (no damage / no unauthorized repairs) plan.