What Pre Norman Coin Would This Be?

It's a coin of Venice. Reading the doge's name will be difficult.

Stonewall, I agree with the others that your coin is Venetian. More specifically, it is a Soldino--it should be about 15 mm or 16 mm in diameter and weigh about 0.5 g (intact, perhaps a little less since yours has some rim damage). The Venetian Doges seem to have used three different types of lions: rampant, nimbate, and winged ("in moleca" in Italian). Here is a list of all the Venetian Doges who minted Soldinos with winged lions:

Andrea Contarini (1368-1382 AD)
Michele Morosini (1382 AD)
Antonio Venier (1382-1400 AD)
Michele Steno (1400-1413 AD)
Tomoaso Mocenigo (1413-1423 AD)
Francesco Foscari (1423-1457 AD)
Cristoforo Moro (1462-1471 AD)

Of this much I am sure: your coin dates to between the late 14th and late 15th Century. In looking at the inscription on the rev (the lion side), you can see enough letters to recognize S.MARCVS VENETI. Unfortunately, this is the same for all of these coins. The inscription that we really want to read is from about 1 o'clock to 9 o'clock on the obv and that is virtually illegible. I do note that to the right of the Doge are the mintmaster marks. In your case a star over a lower case R. In looking in Biaggi and the interwebs, I can only find one of these coins that has this specific combination: Michele Steno. I do note that the pics from Biaggi are pretty rough and not every coin is even pictured anywhere on the net. Therefore, my best guess is that your coin dates to between 1400 and 1413 AD and was minted under the authority of the 63rd Doge: Michele Steno. I would attribute it as Biaggi #2860. The obv inscription should read +MIChAEL.STEN'DVX. If I squint, the last two letters before the dot at about 5 o'clock certainly could be E and L. Then, at about 7:30 when the inscription picks up again, the first letter really looks like an S. This certainly could be our match...I'm only about 90% sure about this--it seems as though several other mintmaster marks were also used by Steno, including a star over a C and a star over some weird button-hook thing.