I dont use it myself Simon but theres a bit in File called Options that has a box you can untick to stop reminders from showing if calendars not running.
I cant see anything else about it in the program though.
I found that bit, Sandra, but as you say, the options are limited.
Can't you just take it out of your start up list? 
A couple of good things if you haven't discovered them yet are the easy partitioning Link and the snipping tool is better than most screen captures 
If I took it out of the startup list, the reminders wouldn't work either, would they?

I'll have a look at that partitioning tool, thanks John. This came pre-partitioned. It's a 120Gb hard drive,partitioned 50/50 for Programs / Data, but I don't need all that much for programs.