I couldn't help laughing.

我忍不住笑出来。

You're pretty close.

你的答案相当接近了。

There was too much work for our computer to cope with.

我们的计算机要做的工作太多，简直应接不暇。

He made an impressive speech.

他发表了一篇感人的演讲。

He made good in business.

他事业成功。

But personally I believe a business letter should end with Very truly yours, not Sincerely.

还行，乔治。但是我个人相信一封商业信函应该以“敬上”结尾，而不是“谨启”。