Time for a New Computer... Suggestions?

My current one is almost 10 years old, and last last me well. But I think it's time to upgrade. It's developed an issue where it powers on for 2 seconds, then turns off, forcing me to plug the power cord in somewhere else before it will attempt to power on again. Eventually, it stays on for good. I think it's a PSU issue, but don't believe it's worth the time or money to try for a new PSU. And I need to upgrade anyway...

With that in mind, let me list some of the things I am looking for:

Able to stream and play 720p and 1080p video
To hook it up to my TV at times to stream video to it
Relatively quiet as can be
Possibly wifi enabled (or ability to add wifi capability later)

I'm not any sort of gamer, so I don't care about high end stuff or being able to play any of the top games on the market. I mainly use it for writing, browsing, and watching stuff. My budget is about $500, give or take. I'm not entirely comfortable putting something together on my own; mainly looking for advice of what to look for in specs, make, models, company, etc. And what to avoid.

I plan to get a new monitor, too, but that's a more future thing. I'd rather get a decent computer now, before my current one dies on me.

Thinking something with a 2-3ghz processor, 2GB+ RAM, and 500GB+ HDD. Any suggestions? Good deals? Things to avoid?