Too much power for extension cord usage?

Let me start off by saying I am not computer savvy.

I purchased a desktop gaming rig online a few years ago, and choose some high end parts as I wanted to be able to play the newer games. The computer ran perfectly, until one day when I went to turn it on. There was a loud click, and then nothing. She was dead. After doing some searching, it seems my power unit fried. I also discovered that the breaker in my panel box had popped. I'm not sure if a surge came FROM the computer out and popped the breaker, or if a surge came IN, got past the breaker and fried the power unit while popping the breaker at the same time, or what. I recently discovered that the outlet where I had my tower, monitor, gaming table, and speakers plugged in ALSO carry lines from our washing machine and a few other things (thanks, Dad).
I haven't yet replaced the power unit as I'm nervous to do so, and my bedroom was being overhauled so it's been sitting under some tarp for now. But my question is, can I run my tower through an extension cord to a nearby outlet that only has a lamp running on it? I'm assuming I'd need a cord and power bar rated for the power of the unit. I'm thinking separating the tower from the rest of the equipment (monitor, etc) to allow the full circuit to carry only the tower.
Advice greatly appreciated.

Build details as follows:

phillpower2 said:

A PSU with no brand name attached is like playing russian roulette when you know that there is a bullet in every chamber of the gun, you just don`t.

For the hardware in your rig you need a minimum of an 850W Gold efficiency rated PSU from one of the following, Corsair RM range, EVGA, Seasonic or Super Flower.

No problem with using an extension lead but be sure to use one that has surge protection as standard.

As is always advised, see if you are able to borrow an appropriate PSU to swap in for testing purposes, if this is not possible, get the rig tested by a local tech or tech store before purchasing any new PSU etc.

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Thank you! They sent me another PSU to replace the one that went, but it's the same type. I'll see about purchasing one of the ones you mentioned and installing that.

Well, I thought if the power supply was too weak, then the exact same replacement wouldn't work either. However, when I went and looked at what they sent, it's actually what you suggested: a Corsair RM850e Fully Modular ATX 3.0 300W PCLe 5.0Power Supply, with a little icon in the corner saying Gold Experience.

I'm thinking it's not so much the power supply as the circuit I was using, it being overloaded. Otherwise why would the breaker pop?

Bruce said:

Another other concerns?

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I'm sorry?

Bruce said:

As in was there anything else you were chasing as I thought it was all wrapped up in post #3.
The new power supply should solve your issues, very good chance the circuit breaker tripped due to the old PSU failing.
We still don't know what the old PSU make/model is?

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Oh, sorry! The old PSU is the exact make/model as the replacement, the Corsair.

phillpower2 said:

As you will be aware electrical current can go in two directions, forward and clean or backwards and dirty when the current hits a dead end, the original PSU being the potential dead end and forcing the charge backwards to the breaker.

Suggest that you test the original PSU using the method shown at Corsair here, no need for the fans just disconnect everything from the PSU to the other PC hardware.

While inside the case look for any scorch marks, bare wires, any loose screws rolling around basically anything that may have caused a short circuit.

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Thanks! I actually didn't know current could go backwards (though I DID suspect it, which is why I asked), and what you said made sense. I'll test the PSU as you suggest.

I'll also lighten the load on that breaker by rerouting some of the lesser powerful things to the other outlet just as an extra precaution (speakers, etc).

Thanks for your help!