one thing i have had happen with one of those type of carts (it was a codemasters micro machines cart in fact) is the nes just kept resetting (the power light blineked as if no cart was inserted at all)
i opened up the cart and found the problem almost instantly, the connector when you pulg the nes cart into just fell off, there was only 20 of the pins used on this one though, so i removed the broken pins and took some of the pins out of the centre, replaced the pins and resoldered the cart back onto the connector and it worked fine after that
and yes, it doesnt sit down in the nes, just sits half in the slot