I am not aware of any available software that would give you the shutter count for Canon 350D.
I have used before EOSInfo Utility but I am afraid it only supports 40D, 50D, 450D, 500D, 1000D and 5DmkII. I tested it on 40D and 450D and it worked fine. Based on the notes on the EOSInfo website it seems that this information is not available for other models
The shutter count information is available only on Canon DIGIC III/IV DSLRs except the 1D* series. This means that EOSInfo will display the shutter counter for the 40D, the 50D, the 450D, 500D, and the 1000D. It will also show the shutter counter for the 5DMkII, but the camera must be power-cycled before the value is updated. The shutter counter will not be displayed (or will be displayed as "0") on the 1D*, 5D, 10D, 20D, 30D, 300D, 350D, and 400D. It's not that I have anything against the owners of those cameras, but simply that the Canon SDK does not support retrieving the shutter count for them. UPDATE (08/06/2009): Apparently, Canon has removed the facility for checking the shutter count on the 500D. More news when I learn something.
I am not sure if this refers to the EOSInfo software or the availability of that information in general