Two main options if you do not have HDMI in on the laptop (doubtful).
http://www8.hp.com/h20195/v2/GetDocument.aspx?docname=c03958367 would appear to be a listing of the specs of that broad model of laptop, mostly they only vary in hard drive, ram and stuff like that rather than expansion options. I do have to note the screen is only 1366x768 (1080p is 1920x1080) but that is still enough for some games.
1) You rip off the screen and either hope there is an adapter to turn it into a more common type of input (far more common these days than it was even 5 years ago), if you are good you might even be able to make some kind of external lead/switch. I can't be bothered to figure out what screen it uses and if there is an adapter for it right now though.
2) Some kind of capture card. If you have a PCI/PCIe slot then there are many great options for capture cards, such things tend to only exist on laptop docks though. To that end you get to consider firewire, USB or PCMCIA/expresscard options, none of which are all that good and none of which are all that cheap when compared.
Do not buy anything that is USB2.0 HDMI capture at this point (they were either DVRs with a USB port or something horribly custom), USB3 has some more options and ones I would actually consider though I will have to go looking before I give proper suggestions ( I would probably start with something like
http://www.markertek.com/product/bm...tle-10-bit-hd-sd-editing-solution-for-usb-3-0 )
Firewire... I guess there is some stuff out there.
PCMCIA/expresscard which does not appear to be on that laptop. Best option if you could have done it though.
Depending upon what card you are using you might also have to have a HDCP stripper in line with it as various consoles do enforce HDCP at various points, fortunately the HDCP master keys were leaked and HDCP strippers are readily available, though you will instead want to search for HDMI splitter and check if the one you are shipping out of China is one of the models that does it.
Note also that if you want to play games you may have to account for lag in your capture setup.
Short version is there are any number of screens with HDMI in out there, probably best to go for one of those.