Yes, Ryzens with G at the end have a graphics card

The cheapest new board is around £60 but for that you need to buy a new case - around £40. Alternatively, you can look for used parts in your area

https://www.amazon.com/MSI-B450M-ProSeries-Motherboard-Crossfire/dp/B0868T19PS

https://www.amazon.com/ZEUS-GAMDIAS-Computer-Motherboard-Excellent/dp/B0BJJ485PN