If it's the motherboard, then you need a new one. There isn't any real way to go about fixing problems with motherboards. When they go, they go. And when they do, it's cheaper to buy a new computer by the time the unthinkable happens. And in the end, any technician is going to tell you that you need to just start fresh.
I am assuming that your computer was rather old. Although, if it isn't relatively speaking, and was within the 3 year warranty for the hardware, you could go directly to the motherboard's manufacturer and try and get them to replace it.
Typically you need a new power supply when you purchase a new motherboard. And that generally means a new case to fit the NEW board in, and the power supply is usually sold with the case, and rule of thumb is that it is cheaper to buy case and power supply bundled together,than buy a case and power supply separately.
After that graphics and sound cards, which are also not that expensive this day and age need to be added in.
However this is relatively optional if you are trying to save money on the initial build. These days most motherboards have a 128mb minimum GPU/soundcard integrated that is completely capable of playing most, if not all older games smoothly. You wouldn't be able to play the latest releases until plugging in a dedicated GPU. But that's easy enough to do if you make sure to get a motherboard with at LEAST one open PCI slot.
Soundcards are optional. Unless you plan on rocking a high end surround sound system,then the integrated soundcard should be fine.
At that point you are left with hard drives, and disk drives, monitors, and user interfaces (mouse/keyboard/ect) all of which you don't *NEED* to buy new, and unless the HD/DDs were damaged by the motherboard's untimely demise, then you can just plug those in and install your operating system and go.
And as a side note motherboards in themselves aren't too expensive, and you can find good deals.
http://www.google.com/products/catalog?q=motherboard+prices&oe=utf-8&rls=org.mozilla:en-US
fficial&client=firefox-a&um=1&ie=UTF-8&cid=5274975187778370967&ei=SsrkS5SKMJHQtgPj-ZnRCw&sa=X&oi=product_catalog_result&ct=result&resnum=4&ved=0CDEQ8wIwAw#ps-sellersYou can get a GOOD high end gaming rig for $900.00 =/- Possibly cheaper if you build it yourself.
May want to present some of this reasoning to your parents. Do some price searching for components on newegg, or go to your local computer store and get a quote on a build.
Ran me $1000 evenish with taxes. $960 or so before. If I can find the price sheet I'll copy it onto here. But anyways here's my build. Take it to a computer shop and ask them what it'd cost you to have them build.
Manufacturer:
INTEL_
Processor:
Intel(R) Core(TM)2 Duo CPU E8500 @ 3.16GHz (2 CPUs), ~3.2GHz
Memory:
4092MB RAM (Corsair?)
Hard Drive:
250 GB
Video Card:
NVIDIA GeForce 9800 GTX+
Monitor:
Generic PnP Monitor (HP1730)
Sound Card:
Realtek Digital Output (Realtek High Definition Audio)
Speakers/Headphones:
Either
Keyboard:
Standard PS/2 Keyboard
Mouse:
PS/2 Compatible Mouse
Mouse Surface:
Table
Operating System:
Windows Vistaâ„¢ Home Premium (6.0, Build 6002) Service Pack 2 (6002.lh_sp2rtm.090410-1830)
Motherboard:
GIGABYTE
Computer Case: Dunno, generic.