AMD Radeon HD 5570 in Dell 531s

I have a Dell Inspiron 531s slim tower desktop. I installed an AMD Radeon HD 5570 graphics card that worked great the first day but then refused to boot. When powering on, the fan noise/speed would go into high overdrive for 10-20 seconds until the power just cut itself off. I removed the card and the system now powers on okay -- except that if it is standing upright, it will go into the high overdrive again but will immediately calm down if I lay the tower on its side. What does this mean and how I can I fix it? thanks!

As a follow up, I installed the "Open Hardware Monitor" to see what was going on and it shows that when the computer tower is laying on its side, the temperature of the two cores (AMD Athlon 64 x2) hovers in the high 50s to low 60s range. As soon as I stand the computer up, the temperatures jump to the high 80s, low 90s. The computer has worked without incident for years in the standing up position.