BRAND new doesn't mean much these days... especially if it was some cheap off-the-shelf DELL special from Walmart or something.
It's probably got a crappy onboard video adapter or something. Without knowing what hardware is in the machine it will be anyone's guess as to the problem. Also, 1024x320 is far from a huge texture/image really. I have used MUCH larger in Construct than that with no issues.
Unfortunately there is no easy answer to the problem, but I'd put money on that computer having a crappy video card.
Also, updating the drivers for the video could fix it... even new computers still use old-ass drivers. When I bought my video cards, the driver in the box was 3 months old. Always get the latest version from the manufacturer or reference manufacturer website.
Yes I totally forgot about that Alspal... I bet the video driver is stretching the image to 1024x1024.