Are there consequences of using PSU that didn't meet minimum requirements?

Hello. I have GTX 260 and the idiots put 390 W power supply. My computer randomly shuts down when playing games so i stopped playing high profile games. I will get a new PSU, but they don't have it in stock now, i will have to wait after New Year. I can play some older games without computer shut downs, but i have the same problem with all of them. First off they all have really bad shadows. Secondly objects just appear when they get close to you. Out of nowhere. One second they are not seen and poof they appear. Also there is no detail on character models and objects away from you.

Well my question is. Will this problems perish when i change my PSU or the insufficient power has permanently damaged my card and i have to ask a new one?

Thanks to anyone that bothers to respond and sorry for badly constructed sentences my English is not so good.

Hello. I have GTX 260 and the idiots put 390 W power supply. My computer randomly shuts down when playing games so i stopped playing high profile games. I will get a new PSU, but they don't have it in stock now, i will have to wait after New Year. I can play some older games without computer shut downs, but i have the same problem with all of them. First off they all have really bad shadows. Secondly objects just appear when they get close to you. Out of nowhere. One second they are not seen and poof they appear. Also there is no detail on character models and objects away from you.

Well my question is. Will this problems perish when i change my PSU or the insufficient power has permanently damaged my card and i have to ask a new one?

Thanks to anyone that bothers to respond and sorry for badly constructed sentences my English is not so good.

Revan_911