Engine failure due to not changing the oil for a long time

First off, the oil light coming on means you don't have enough oil pressure, which is usually caused by not enough oil. So rather than adding a quart or two, you continued to drive it for a week. Not a good call, my friend. I doubt driving it for a week led to clogging; rather it's more likely that there just wasn't enough oil in the pan to provide lubrication to the parts that needed it.

Your choice to repair or replace is going to be mostly an economical one. Your cheapest option would be to buy a used engine from, say, a wrecking yard and replace it.

Next in line would be repair, but that will likely be rather expensive; you'll almost certainly need to replace the crankshaft bearings, probably have the crankshaft machined and it's possible there's camshaft damage as well, which could require anything from machining to replacing the camshaft and/or the cylinder head. The cylinder walls will have to be checked for scoring and could need to be machined out, resulting in needing oversize ring or piston replacement.

As expensive as an engine rebuild can get, it's still likely cheaper than the cost of a new engine, although it may be possible to get a rebuilt engine for a comparable, or even lower price than repairing the existing motor.

You should probably have a qualified mechanic assess the damage to your engine so you have someplace to start. The damage may not be too severe, making repair a viable option, or it may be catastrophic, whereupon you may need to consider your replacement options.