Your motherboard manual should have some info about it, so have a look in it. Or, if you don't have one, tell us the make & model of your motherboard - a PDF manual or related info could be available on the Internet.
If we cannot find any info about it, I'd try disconnecting the auxiliary cable & seeing how it does with the direct cable only. If it doesn't run, connect both cables. It's safer to supply less power initially than too much power.
But before doing so, tell us the details of your new graphics card & your PSU's make & model number (or wattage). If the PSU is not powerful enough, you could cause damage to it & the components it's powering. G