I read this topic with interest, my bf and I don't really ever argue but I think it's valuable to read advice and have a healthy attitude if it ever does happen.
The observation I would like to make is that in my experience outside my LDR, it is ridiculously easy for there to be miscommunication if using IM type programmes to communicate. With friends, I'd get the wrong end of the stick or we'd misunderstand what the other was saying etc. Phones or skype voice calls are much better but honestly, nothing can beat video calling. When my bf and I first started video calling we never looked back even though we'd never argued before that anyway. We hadn't met in person then, just emails, voice calls and photos. At first I was doing full hair and makeup before every call :p within days we'd seen each other at our very best and very worst and were even more in love than before. Seeing his expression as he talks and watching him smile in reaction to something I've said is just amazing. It's like being in the same room together. I would definitely recommend you try it if you are having silly arguments using IM.
Now we only ever use IM if we're typing messages to each other as we are on a video call, or if one of us isn't at their computer and we just want to leave a little message for when they get back
The phone is only if one of us is away from home or the internet is down.
Something I will say though is that being in a LDR, as we all know, is tough at the best of times. If you can't resolve disagreements quickly and without the slightest trace of ongoing resentment, you are heading for trouble. Without a doubt. It's the same in any relationship, but long distance? Nightmare. I totally agree with the advice not to sign off until you've tackled athe problem and completely cleared the air. Like I said before my bf and I haven't had arguments but sometimes one of us will be a little sad or down, almost always because we're feeling the distance and counting the days until we get married in May or when my bf's father is very ill or just because we've had a bad day! It's frustrating not to be there to administer hugs and TLC to the person you are in love with when they're upset. Times like those are an opportunity to prove to each other that we're in it forever, not just for the happy cheerful days, but there to support each other through the tough times too.
I really hope it works out for you!
Good luck.