Can you put a core i7 processor in a dell dimension 4550

Only if you also change the mobo and memory, as the i7-860 needs a different socket than the 4550 has - it won't even take the older core 2 duo processors - at best it will take a Pentium 4. The BIOS also will not support dual core processors let alone quad like the Core i7.

No offense, but pairing an i7-860 with 1GB of RAM would be a horrible balance either way. You shouldn't plan on keeping the computer at all, but either build a new one yourself from scratch (slightly more expensive, depending on where you live) which will give you a lot more flexibility and better quality parts, or just buying a new branded PC like Dell (if you don't plan on doing much with it, and are fine with basic hardware). I'd say it would be a good idea to lurk forums and check the suggested builds for $xxx to get a feel for what's out there, and more importantly, understand why decisions were made so that you have the flexibility to make better decisions for your own situation (cost/use of computer).