I recently bought a new HP DV6-3118SA laptop, but I am having a very discouraging problem with the graphics card. The graphics card is Radeon Mobility HD 5470. It doesn't install by default, but I do get some message suggesting to install the driver. If I install that driver, the next time I reboot, the screen goes blank and that's it! The same happens if I install the proprietary driver (fglrx) from ATI website.

Could you please help me with this?

EDIT: Following @Ronald and @Oli advice, I am dumping the output of lspci -k:

00:00.0 Host bridge: Intel Corporation Core Processor DRAM Controller (rev 02)
    Subsystem: Hewlett-Packard Company Device 144a
    Kernel driver in use: agpgart-intel
    Kernel modules: intel-agp
00:01.0 PCI bridge: Intel Corporation Core Processor PCI Express x16 Root Port (rev 02)
    Kernel driver in use: pcieport
    Kernel modules: shpchp
00:02.0 VGA compatible controller: Intel Corporation Core Processor Integrated Graphics Controller (rev 02)
    Subsystem: Hewlett-Packard Company Device 144a
    Kernel driver in use: i915
    Kernel modules: i915
00:16.0 Communication controller: Intel Corporation 5 Series/3400 Series Chipset HECI Controller (rev 06)
    Subsystem: Hewlett-Packard Company Device 144a
00:1a.0 USB Controller: Intel Corporation 5 Series/3400 Series Chipset USB2 Enhanced Host Controller (rev 05)
    Subsystem: Hewlett-Packard Company Device 144a
    Kernel driver in use: ehci_hcd
00:1b.0 Audio device: Intel Corporation 5 Series/3400 Series Chipset High Definition Audio (rev 05)
    Subsystem: Hewlett-Packard Company Device 144a
    Kernel driver in use: HDA Intel
    Kernel modules: snd-hda-intel
00:1c.0 PCI bridge: Intel Corporation 5 Series/3400 Series Chipset PCI Express Root Port 1 (rev 05)
    Kernel driver in use: pcieport
    Kernel modules: shpchp
00:1c.1 PCI bridge: Intel Corporation 5 Series/3400 Series Chipset PCI Express Root Port 2 (rev 05)
    Kernel driver in use: pcieport
    Kernel modules: shpchp
00:1d.0 USB Controller: Intel Corporation 5 Series/3400 Series Chipset USB2 Enhanced Host Controller (rev 05)
    Subsystem: Hewlett-Packard Company Device 144a
    Kernel driver in use: ehci_hcd
00:1e.0 PCI bridge: Intel Corporation 82801 Mobile PCI Bridge (rev a5)
00:1f.0 ISA bridge: Intel Corporation Mobile 5 Series Chipset LPC Interface Controller (rev 05)
    Subsystem: Hewlett-Packard Company Device 144a
    Kernel modules: iTCO_wdt
00:1f.2 SATA controller: Intel Corporation 5 Series/3400 Series Chipset 4 port SATA AHCI Controller (rev 05)
    Subsystem: Hewlett-Packard Company Device 144a
    Kernel driver in use: ahci
    Kernel modules: ahci
00:1f.3 SMBus: Intel Corporation 5 Series/3400 Series Chipset SMBus Controller (rev 05)
    Subsystem: Hewlett-Packard Company Device 144a
    Kernel modules: i2c-i801
00:1f.6 Signal processing controller: Intel Corporation 5 Series/3400 Series Chipset Thermal Subsystem (rev 05)
    Subsystem: Hewlett-Packard Company Device 144a
    Kernel driver in use: intel ips
    Kernel modules: intel_ips
01:00.0 VGA compatible controller: ATI Technologies Inc Manhattan [Mobility Radeon HD 5000 Series]
    Subsystem: Hewlett-Packard Company Device 144a
    Kernel driver in use: radeon
    Kernel modules: radeon
01:00.1 Audio device: ATI Technologies Inc Manhattan HDMI Audio [Mobility Radeon HD 5000 Series]
    Subsystem: Hewlett-Packard Company Device 144a
    Kernel driver in use: HDA Intel
    Kernel modules: snd-hda-intel
02:00.0 Network controller: RaLink RT3090 Wireless 802.11n 1T/1R PCIe
    Subsystem: Hewlett-Packard Company Device 1453
    Kernel driver in use: rt2800pci
    Kernel modules: rt2860sta, rt2800pci
03:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168B PCI Express Gigabit Ethernet controller (rev 03)
    Subsystem: Hewlett-Packard Company Device 144a
    Kernel driver in use: r8169
    Kernel modules: r8169
7f:00.0 Host bridge: Intel Corporation Core Processor QuickPath Architecture Generic Non-core Registers (rev 02)
    Subsystem: Hewlett-Packard Company Device 144a
7f:00.1 Host bridge: Intel Corporation Core Processor QuickPath Architecture System Address Decoder (rev 02)
    Subsystem: Hewlett-Packard Company Device 144a
7f:02.0 Host bridge: Intel Corporation Core Processor QPI Link 0 (rev 02)
    Subsystem: Hewlett-Packard Company Device 144a
7f:02.1 Host bridge: Intel Corporation Core Processor QPI Physical 0 (rev 02)
    Subsystem: Hewlett-Packard Company Device 144a
7f:02.2 Host bridge: Intel Corporation Core Processor Reserved (rev 02)
    Subsystem: Hewlett-Packard Company Device 144a
7f:02.3 Host bridge: Intel Corporation Core Processor Reserved (rev 02)
    Subsystem: Hewlett-Packard Company Device 144a