Looking for IT Inventory Management Software

Hello Everyone, I am a learning at the job IT Administrator (I'm the SQL DBA-and don't really have credentials for that either, just classes I've take). So to say the least I've done a lot of research to find answers and then also ask questions in Forums to back-up my research. I work for a not-for-profit group so we have little money to spend on IT unless we REALLY need something. I have heard that there are programs out there that can run on one computer and inventory both hardware and software of all computers on a domain. I'm looking for either a free or inexpensive one to run at my company. Does anyone have any suggestions of some of the products out there? I thank you in advance for any assistance!