Is my PSU underpowered?

So, here's the deal... I've got two setups that aren't quite working right, so I’m thinking about doing some tinkering here and there.
I'm considering swapping a 350W power supply into a build that used to have a 420W one before it died on me.
The specs are

A Seagate 500GB HDD plus another 160GB drive—no clue what brand—but I need both since I'll have Windows on one and my data on the other.
An Intel Core i5 Pentium Dual-Core running at 3.2GHz.
An ATI Radeon HD4650 with 1GB of DDR2 memory.
4GB of RAM (DDR3 2 x2).
Some random LG optical drive, which is pretty much a necessity.
An AsRock G41 motherboard, though I can't remember the exact model.
And that little 80mm fan.

Basically, can that 350W unit actually handle this? I don't really want to take the risk and end up frying everything, but buying new parts is totally out of the question for now. I'm just trying to cobble together this junk I already own, at least for the time being.

Also, one more thing: the fan on the graphics card is way too loud. Is it okay if I just rip it off and point an external fan directly at the card instead?

If it isn't totally trashed, it should run fine. What brand is it, and how old are we talking?

Regarding that FS group, I can't give you the exact details right this second, but it's looking pretty solid. It’s about 3 years old now.

If the unit is actually functional and you're dealing with an FSP power supply, it should hold up just fine. Honestly, my advice? Pop the heatsink off the graphics card, give it a good cleaning, and slap some fresh thermal paste on the chip.

Check the sticker to see the exact brand and model, then let me know. There's no sense in gambling on this—it’s just not worth the risk.

Even a cheap 300W unit would handle this easily since it barely pulls 100W total—given we're looking at a 65W CPU and a 35W GPU. It seems to be some entry-level Fortran model, maybe from the PNF or APN series, so I guess there isn't much to worry about.

So, I’ve got an FSP Group power supply in there. Everything's hooked up and running smoothly... I just haven't connected those front panel USB ports or the headphone jack yet since I don't have the manuals for either the motherboard or the case.

Does that mean I should pull off the whole heatsink? And that metal piece too? I tried, but it wouldn't budge, and I really didn't want to force it and rip anything out. I mostly just play Euro Truck Simulator 2, so would it actually work without a fan? It wouldn't be a huge deal to swap in a different one if it's absolutely necessary.

thanks guys

I guess you might be able to get away without a fan on that GPU, but maybe try pointing one at it just to see what happens. Run a game and check your peak temps using Open Hardware Monitor running in the background.