@JetJockey01 , welcome to the Community.
It believe the model of your computer is TP01-1026, The motherboard in your computer is HP proprietary. It has a 4-pin power connector instead of a standard 24-pin ATX power connector. You will have to buy any PSU upgrade from HP. HP has a 400W PSU (L69242-800) that should be compatible with your motherboard. You can order it on HP PartSurfer by clicking the box next to "Add to Cart". Here is a Power Supply Cross Reference Chart that will show you where I got this information. Your exact model is not listed, but it shows a Baker motherboard in the TE01 series.
HP has a 500W PSU (L5757-800) that may be compatible, but you would have to contact HP Customer Support to make certain.
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I am not an HP Employee!!
Intelligence is God given. Wisdom is the sum of our mistakes!!