I understand that you cannot hear the CW. Are you deaf or tone deaf?
I once knew a ham, a silent key now, that used to put his hand on an open speaker to feel the cw. He operated about 30 wpm. Not suggesting you go so far, but that is an option for learning the code. It may take the FCC many years to change the code requirement. As for the test, you may wish to petition the FCC for a waiver based on your handicap. Just my $.02. A couple suggestions in case you haven't heard of them.
As for a contesting rig, what kind of contesting are you considering?
I would guess that the two most important features of a contesting station are the antenna and the capabilities of the rig. The most important being the antenna - hearing and being heard.
The rig needs to be compatible to your mode. If you are using RTTY, you need a rig capable of handling full power continously as opposed to one that needs to have power reduced to operate. The next most important thing is speed - being able to change frequencies quickly and easily. I don't recommend a Swan (the rig I have) as you would need to re-tune it every few kcs and changing bands takes a while.
You might consider a dual vfo rig. Look for contacts on one vfo while making contacts on another.
Of course solid-state rigs are best suited for contesting especially for QRP. You might consider an automatic antenna tuner and/or a medium power amp for 500-700 watts. I still think the antenna is most important tho as it will amplify both incoming and outgoing signals alike.
If this were me, I would find the best price on a decent all-band, all-mode rig I could find and then look for the best antenna I could find for my lot. Then I would put it in my budget to get that antenna. Later, if necessary, I would work on the highest practical tower I could get.
I like the Icom brand, personally but Kenwood and Yeasu are good too. I am sure many other brands are good as well. You'll have to make your purchase based on the combination of warranty, features and reliablilty of radio.
Good luck in the contests!