A few things, your CPU is the component which would host the on-board graphics not the motherboard. Intel CPUs that do not have an -F in their model number have on-board graphics (11400 or 11600K for example) so knowing what model you have may clarify this.
I assume that the system is no longer able to POST even with the new graphics card installed? This likely indicates that it is an issue with the motherboard itself potentially having a damaged connection to the GPU (just a guess). It would also be helpful if you have a recording of the beeps to help you confirm the pattern.
Assuming that you're US-based and that this machine is primarily for gaming, there are a few questions for you to think about:
- What budget are you targetting as your $ ceiling?
- What monitor are you pairing this system with / what resolution do you plan to game at ?
You may find more value (fps/$) in going for a slightly lower tier CPU, and nvme storage and upgrading the GPU
I haven't fully attempted this yet however this appears to be achievable on Android via Tasker using the Voice Command Capture project in combination with a remote control app - I'm using Unified Remote which features a Wake on Lan command which I've setup and know to work.
Hope this helps!