'93 Passat engine trouble

2.0L Passat starts sometimes, and then will idle roughly and stall. Or it will start and only keep running at high RPM (3-4K or higher). Engine has been overheated, but compression shows consistent ( 120-190-190-190), so I am not sure where to go from here. The battery is dead and will only start when jumped, so could the low power cause this scenario? Just wondering where to look next. Thanks.

Matt