What was your previous used GPU card?
Be sure to un-install all old drivers and clean-up with a registry cleaner (e.g. CCleaner).
Do you have no signal when booting up to your Windows system, or no signal right on by pre-post (even not allowing to go to BIOS)?
When having no signal, do the cooling fans spin of your 7870 ?
Greetings, Babylonia
GPU: Sapphire HD-7770 Vapor-X, MB: Asus P8Z77-V PRO, i7 3770K, Corsair Vengeance 16Gb RAM, Intel SSD 520, 2x SSD Samsung 840 Pro, BlueRay: LiteON R/W, HD: WD Black 1TB, PSU: 620W - 12v 50A...........