Jesse has been getting rather steamed up about COM+ and state. Here is my advice:
If you want to use COM+ and all the benefits that that brings (scalability through JIT activation and object pooling / ACID transactions across multiple data sources / Queued Components / SOAP support etc etc) then embrace the stateless model that COM+ requires.
Pass all parameters in on the call.
Small bits like connection strings can be setup in Component Services manager using Object Construction. If you really must keep state there are options such as the Shared Property Manager or deserialising and reflating objects using SQL Server or file storage (.Net serialisation makes this easy).
An important question you should ask. Why do I need COM+? All this cool stuff means overhead. It is only recommended for large enterprise apps with very high numbers of concurrent users.
Above all remember that COM+ is not a small thing to be mastered in an afternoon by cutting and pasting a few lines of sample code. Read, code and learn and if it gets tough, then console yourself that you are gaining a very valuable skill.