I have an old Dell Dimension E510. When I press the power button, it makes noises like it's turning on, the hard drive's whirring, the fan's spinning. But the power light blinks orange. This seems to be a common problem with Dell Dimensions, but with me, after quite a long time it boots up fine. Sometimes it says it failed to start properly and asks if I want to use the last known GOOD configuration or start Windows normally, I usually say "start windows normally," and then it boots up and everything's fine (it's running Windows XP, which I know is old). I've only heard of them not turning on at all, but mine simply takes a while in the blinking state.

Could it be a software problem, since it says it failed to start? It sounds more like a hardware problem to me, since it blinks orange before anything boots. From what I've read it's usually a PSU issue, but is that not the case since it runs fine afterwards? I'd like to try a different PSU, however my only other computer has a 250w PSU according to the specs, while the E510 uses a 305w PSU. Can I just buy any 305+ watt PSU and connect it? If not, can you please recommend one (hopefully as cheap as possible)?

It has an Intel Pentium 4 CPU and 1 GB of RAM. Not really sure what else you might need...Flakey PSU...yer probably right on in your guess...
However i wouldn't go out and buy 1 for an old PC...i'd borrow a known good one from a friend...and swap it in there overnite...
You'll know by morning...I don't have any friends with PSU's to borrow. eBay has been kind to me with all of my electronics needs, I just need to know what to look for. I'm new to PC component shopping, any help would be appreciated.

EDIT: Actually I think I found a good one: http://www.ebay.com/itm/SEASONIC-ORIGINAL-400WATT-ATX12V-ACTIVE-PFC-F3-DESKTOP-PSU-POWER-SUPPLY-SS-401HT-/391383288858?hash=item5b20430c1a:g:38QAAOSwiYFXFOLSPower supply pictured looks to be USED. It has scratch marks as though it was installed into a case already and pulled from a build. Description of No Signs of Wear. The PICTURES provided show that its been installed into a tower at some point into a power supply bay that has spring loaded fingers which left scratch marks, so its really a used power supply and not new. However they claim to have 10 available 7 left so maybe you will get a new one vs a used one. Price tag with FREE shipping isnt bad if the power supply is a good one.

I have gotten burned on ebay with power supplies so I  no longer use ebay for power supplies and instead pay about $40 for a power supply with a warranty and easy return plan. Given your system is an old Pentium 4 or Pentium D, I can see cutting corners in cost to fix it, but just sharing that according to description and pictures they are offering these as new and the picture that shows power supply installation scratch marks means that you might be BUYING used. They claim to have a 30 day warranty and 99.5% positive track record so they should be ok.

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New other (see details): A new, unused item with absolutely no signs of wear. The item may be missing the original packaging, or in the original packaging but not sealed. The item may be a factory second or a new, unused item with defects. See the seller’s listing for full details and description of any imperfections.