The bad news is that the specs say the maximum memory per slot is 512mb so it might be impossible to run a 1 gb stick.
The good news is that Dell offers a 512mb stick of pc 3200 memory as replacement memory for the 2350 so you may be able to go for faster 512mb memory. However at $29 a stick, $58 is quite a bit to invest for a modest speed improvement in a computer that age.
In a Dell computer, you have to be very careful in matching memory if you don't buy from them as they don't provide - or at least I am not aware of - a list of compatible memory. They want you to purchase from them. So if you are not matching the make and model already in the machine with just a larger size within spec, you might have a problem. Variables that can affect compatibility include, size, speed, memory timings, and voltage.
The specs only list the pc2100 memory speed, so at pc2700 you are already pushing it over spec - but this should not be an issue since they list the pc3200 for replacement.
The only other thing I could suggest is searching on the Dell forum or other web forums to see if someone else has already done a successful upgrade with different memory - of course you would still neeed to purchase it.
Sorry the news is not better.