Refusing to start - where do I start?

I have a 2001 Renault Clio Alize Automatic, with starting problems.
When I purchased the car (month ago), the key fob never worked but I could open the doors and start the car. Then the starting got a bit tempermental. As it had been of road for a bit, we deceided to change the battery and for a few days the car was fine, with the occasional delay starting it. I realised one key started it and the other did not so continued to use the good key. Until the other day when the engine would turn but not fire up. I had the red immobiliser light flashing away at me on both keys. So called out my breakdown recovery. He didn't even look really, just said it was a key problem, send to Renault or look at scrapping the car!!
Anyway I said leave it on the drive and I'll see. I contacted Renault and they first recommended a lock smith near me which were pretty good, so I went and got another key cut. They cut a standard no fob key. I said I don't care as long as the engine starts. I got home it didn't start. It turned the engine like the other 2 keys but the immobiliser didn't flash on it. Anyway my mechanic come and took it the next day. He got it started with the new key (then the old key started it, but it did cut out around the corner. It took him a while to get it started again but he did and has since started it on and off on occasions.
I would like to have this car back at some point but reading some of the car forums on the internet, I am horrified of what a common problem the old fave clio has starting.
My questions are
Does the key always need that battery fob working to disable the immobiliser?
If it is immobiliser problem, why start sometimes and not others?
Can we bypass the immobiliser and how? Because it does start without the bleeper key, is there a chance it is not the immobiliser? I really dont want to waste lots of money trying 101 solutions that might not even work.
I am trying to avoid going to the dealer as I know I can't afford to. Please help somebody.