If it was a hardware issue it wouldn't of mattered whether it was on boot or once the system was running. Upon boot a power surge is needed to start the components running which is why it was struggling to run with the wireless card just pushing it over the edge.
It was possible to use a workaround which is to turn the psu off via the switch on the back for 10 seconds. Then turning the switch and simultaneously the pc on caused the power surge to be increased and the amps available from the psu are momentarily at a peak above normal operational standards. My pc also runs normally 24-7 and has done for 2 years, my solutions for turning it on were either to unplug the pci wireless card and turn it on or surge the psu. Taking out the wireless card was the easier and quicker option.
That is a budget a case have you looked at the htpc market lately cases range from $70-2000 there is even some special editions which are $10,000. It is made from rolled steel which is the cheapest metal cases are made from, next up is SECC steel, then aluminium frontage and full aluminium of varying grades. Newegg seems to have a rather limited selection of desktop pcs that look more like audio components then computers. [/url]
The retail version of the psu comes with a 3 year guarantee the bundled might not you will only know once you have bought it.