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Which display impressed you - the TV ? or the iPad ?
Beware of impressive tv displays - they've usually got too much contrast and colour and while they look "good" for a while they are rarely accurate for photo work. Then again, maybe your laptop screen isn't either - has it been calibrated and profiled ?
Most new laptops will run rings around your old one thanks to more RAM, faster cpu, quad core cpu, bigger and faster drive(s) (perhaps SSD but even HDDs are faster than those from a few years ago), HDMI output, USB 3 output, etc. Probably runs cooler too.
Try to find one with 132 pixels per inch instead of the more common 110 or 100. It will be noticeably less pixelated but not as nice as the 264 ppi retina screen on the ipad.
I doubt that sitting in front of the tv is ideal for editing photos because of the distractions including the moving colour tv picture above/behind your laptop screen, but I understand why you might want to get away from the office area. Maybe you'll find it better to use a different room or wait until the tv is off.