I have a not so perfect record. Its actually a bit worse than not so perfect. Without having to go too much in detail, do you think it would be impossible to get a good job in electrical engineering with felonies showing on a background check

It will depend on how long ago you were convicted, the nature of the charges, each company's hiring policies, and on the individuals who are making the hiring decisions. Nothing is impossible, but it will probably take longer for you to find a job than for someone who has a squeaky-clean record and you may not get the "juiciest" positions unless you've established yourself in the field as a valuable commodity.

If it's been at least five years since your convictions and your record is clean since then, you will want to consider hiring a lawyer to try & get the convictions expunged from your record. If you can do so, it becomes a non-issue... and the money invested in your lawyer's fees will be a great investment.