I'm going to give you a less critical (and it turned out much longer!
) answer than some others here. I think you might be able to develop some basic competency at some martial arts techniques by practicing at home with a partner,
if you watch the right videos and reading reputable books and
if you work hard and are dedicated about practicing. But I think, even with hard work, your results are going to depend a lot on both the quality of resources available and the kind of thing you're trying to learn, and are still going to be limited if you don't have access to feedback from an instructor.
For an example, you say you have some TKD experience. If you want to further that, Kukkiwon has a ~$150 DVD set showing all the WTF/KKW forms in painstakingly thorough detail, and I think if you have some experience, you may be able to teach yourself the forms adequately by watching the video, following along, and then filming yourself and comparing yourself to the person in the video. (Edit: But if you're just imitating movements, you may miss things that are important but don't seem to be, misinterpret what the movement is supposed to be, etc.) I've also seen some decent tutorial videos on youtube from a user called, let's see, "Learn Taekwondo Online", and I think you could probably learn at least the concept of many strikes from watching these kind of videos. Make sure they're good videos though, not ones with corny titles like "Feral Fight".
But when it comes to sparring, you can't
possibly learn that solo, or even with one training partner. You'll get in a rut. You need to spar with a bunch of different people to improve your skill, and especially with people who're more skilled than you and can help/push you to improve.
And then, when it comes to more subtle grappling techniques... I think you're up the creek there. Even in a class setting, those often require one-on-one instruction to really get right. An inch down the arm or turning your foot a certain way can be the difference between a joint lock working great, sort-of, or not at all. And it's easy, without good instruction, to do "sort-of" and think it's "great" - or to (even unconciously) modify the technique in some way that misses the point.
I also am going to second (third, fourth, whatever) others that have posted about the injury risk of teaching yourself because you're not doing things right. You can mess up your knees doing rotary kicks improperly (not pivoting), give yourself a boxer's fracture not punching right, not to mention spraining your wrist or throwing out your back trying to do some Hapkido/Jujutsu/Aikido kind of techniques. So you have to be careful.
If I were you, I'd focus on getting generally fit, since that's always going to help you, and on drilling basic striking and blocking techniques with BOB and a partner. If you want to learn forms to do a TMA, try it like how I mentioned above.