I've just bought myself a 1999 Vauxhall Tigra, 1.4 Chequers version. I
seem to be having problems with the key/ignition/electronics, and would
appreciate some advice.

When I unlock the door (no problem), get in the car and put the key in
the ignition it won't immediately turn. I fiddle about for perhaps half
a minute before it finally does. On other occasions a similar thing
happens when I try to unlock the boot. Is this normal? Am I doing
something wrong? And what is the beeps I hear just after switching off
the engine and removing the key -- is it the immobiliser coming into
play?

I did contact the seller, an ebay trader, but he reckons that he had no
such troubles (yes, well he would anyway I guess...).

I do have two keys but I get the same result with both. I'd appreciate
any help and advice.