I have a TC33D and am also having a problem with starting it as well. However, my situation sounds a little different than yours, but maybe not entirely. As Soundguy has recommended I would check your electrical connections first. I too had an old/weak battery, which has now been replaced. My scenario went as follows (sorry this a long post):
Turn key to the right into the glow plug position, wait 5 seconds for glow plug light to go out, then turn key further into the spring back position for engaging the starter however my starter never engaged and after trying this a few times I blew my main 30 amp fuse (stupid me).
So, like you I now have a new battery.
After the new battery installation everything seemed to work fine...turn key to the right, glow plug light would come on, after 5 seconds time out, turn key into spring back position, starter would engage and in 2-3 cranks engine would run fine.
So now what happens is when I turn the key to the glow plug position the instrument panel lights up with everything (battery light, oil light, Parking light, etc) except the glow plug light. The 540 & 600 rpm indicators even light up and after 5 seconds go off. Now I turn the key to the spring back position and the starter engages and after about 5-6 cranks the engine begins to run. What's interesting is that when I hit the spring back position the glow plug light illuminates. I thought it was the ignition switch so I took it out and actually disassembled it to find a spring and contact, which was being held up by what appeared to be some, melted plastic. I thought I had cleaned it up and used a volt meter to check for continuity after I put it back together between the 2 sets of contacts and it appeared to be working fine. Except last night when I reinstalled everything I got the same results of no initial glow plug light. Lets just say these ignition switches are pretty flimsy. So while I get continuity with a meter maybe the contact for the glow plug timer first initiation just isn't allowing the required current to flow.
When it comes to electrical stuff I know barely enough to get in trouble so I could be wrong about all this. My next plan for attack of this issue is to replace the switch a more robust metal one from NAPA (like others have done). I could get another New Holland one but then I think it would be susceptible to the same issues.
To answer your question about how to get to the ignition switch you need to remove the section of cowling which it is mounted in by removing the four bolts/screws, which hold it on the tractor. Two are mounted in the left edge of this cowling below the instrument panel between your legs as you are sitting in your seat. The other two are located on the right hand side; you get to them by removing the panel, which your oil dipstick protrudes through. The ignition switch itself it held on with a plastic nut in the front and then there is a 4-pin electrical connector on the back.