The main earth (or ground) connection is on the back of the motor, just above the gearbox section behind the cylinders (the frame is not used for electricals on these bikes, 'cos of the alloy construction). It's worth checking this connection even though it's a pig to get to (even more so if you have the California-style anti-pollution pot there). But if you can, loosen the nut, undo the cables there, vaseline them up and retighten (not too tight).
Also, the starter solenoid under the seat has a large master fuse on it (under a cover) - pull this out and check for corrosion, then also vaseline and reassemble).
But it does sound like your battery might be a bit suspect, even if it's new. There are batteries and batteries, and you need the best you can get for the Tiger. To confkrm if this is the issue, hook up a car battery in parallel via jump leads (N.B. the car engine should NOT be running!), then try starting the bike a few times. If there's no problem at all, you might want to relook at the battery.