Hi Allan!
If you can check IRQ settings in device manager.Usuly COM1 is using IRQ4 and COM2 IRQ3.Maybe you have conflict in IRQ's.If you open Control Panel , System , Hardware Tab , Device Manager , select View , Resources by type , Interrupt Request.COM1 and COM2 shouldn't clash with other IRQ's.
If they are double click on port with same IRQ as COM1 or 2 , on resources tab remove tick on automatic settings and manualy set IRQ.
Use numbers not used by IRQ's ,(5 , 7 , 11 or other).Complicated

Hope it's that.