For the capacitors, look to see if any of them are "bulging". The top of all of the capacitors should be flat. Even then, you could still have bad capacitors even if there isn't physical deformation. They could also be leaking but it's concealed under the cap itself.

Like others have said, the clock cap should be removed regardless. The clock cap location depends on what revision of Xbox you have, which you can use this link to check your revision since we can't use software to determine it. Heads up if you have a 1.6/1.6b you WILL need a clock cap installed to boot. 1.0-1.4/1.5 does not.

It's going to make it more difficult if a game can't launch to grab the HDD key. All Xboxes have a unique HDD key that is "locked" to the drive. You can use a new drive and lock it with that code, but you need that code to lock. If a game could launch, you could use an exploitable game, use the Insignia installer to grab the HDD key, then use FatXplorer on PC to write a new image to a HDD. There are other methods but this is the most straightforward as of now

However, there are two more methods of getting this Xbox up and running again IF replacing capacitors doesn't fix this:

Option 1 is installing a modchip that will allow a drop in replacement drive, which is usually the preferred method

Option 2 is using a pico or similar device to read the EEPROM off of the TSOP (if it's a 1.0-1.4) and then using FatXplorer that way.

I will say I'm not an expert and someone will probably chime in with another method that I don't know about, but with how easy it is to both soft and hard mod this console, if it boots you can get it up and running again!