There is no good way to fix it yourself. What is the secondary error code or the one shown on the screen? E74? E73?
It will need a reball or a reflow using a reworking station. Many people use heatguns to "fix" their xboxs instead, but those people often ruin their xbox beyond repair by blowing capacitors and warping the board.
A reball is the most reliable fix, but a reflow can be reliable too if done right.
You'll need to send it to someone if you want it done right. There are many qualified people on this forum and many others who can perform both services. Myself, I could reflow it for you, but not reball because I haven't purchased a reballing jig yet.
Reballs are usually pretty pricey compared to reflows because they are more time consuming. You can try your luck with a 20 dollar heat gun but that will surely not last forever if the board comes out of it alive.