1. The only thing we know is your PSU is just 480W, we need more info about it's amperage on each rails.
2. HD4870 is a HOT card, i doubt that card cooler can handle the heat, HD4870 can get hot pretty fast.
3. Without knowing more about your PSU, i won't dare to run HD4870 on that PSU.
The HD 5750 uses even less power at 59w, but it's performance is similar to the slower HD 4850. Pretty safe bet that you will not have to upgrade the PSU. Here the lowest priced HD 5750 @ newegg,com at $115 after a $10 mail-in rebate and $5 shipping:
If I got a GeForce GTS 250 for around the same price as the 4850, which is, according to most benchmarks, relatively in the same tier as the 4850, would that just be stumbling right back into the power issue again or would that be a decent alternative to downgrading to less powerful cards?
Also, when I'm looking at cards to upgrade to, should I be looking more intently at the memory size, the memory interface, or the core clock?
By the way, thank you very much for the replies so far, I really appreciate the help.