Further to the very salient points already raised, here is one more:
Do NOT lie or leave out information ... ever
I've been on both sides of tech support and the number of times I have had users try and tell me some tall story about what went wrong is amazing.
Come on people - I'm don't care if it was your fault - I'm just here to help you get it fixed. Don't leave out information so that you won't be blamed for causing the problems. All it does is prolong the fault fixing and increase my 'pissed off' meter. And anyway, in most cases I know what the real cause is. Heck, I'm a system administrator, I know everything that goes on in my box, and if I don't know right now, I'll know in a couple of minutes. Lying or leaving out bits of important information does nothing but piss me off.
On the other side of the coin, let me tell you of my experience with tech support. I had just bought a Aus$2400 (US$1200) Hewlett Packard laser printer for the College where I worked. While not a huge amount in corporate terms, it was a lot of money for a small College. Within two weeks of this printer being purchased, a student manually fed through paper with a plastic reinforced margin. Naturally, the plastic melted and destroyed the toner drum.
On phoning HP tech support, the thought did cross my mind to lie. After all, if a student had destroyed the printer, then our warranty was void. However, I didn't - I told the tech support person exactly what had happened. And this is what the tech support guy said:
"Well yes, you have voided your warranty and unfortunately, the toner drum is the most expensive bit of the printer to replace. However, this is what I'll do. I'll write the fault report as 'toner does not stick to paper'. If you're lucky and the tech repair people don't question it, you'll get your printer repaired for free. If they question it, you will get charged and you will have to pay."
As luck would have it, the tech repair people didn't question it and I got the toner drum (Aus$1000) replaced for free.
The actions of the tech support guy is exactly the sort of thing that I would do if I feel that the customer is genuine, polite and helpful to me. As a tech support person, I want to help you. You help me (by being polite and friendly) and I promise you we will have your problem resolved in no time!